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Discrete Mathematics283(2004)289–293

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Edge choosabilityof planar graphs without small cy cles

Li Zhang?,Baoyindureng Wu

Graph Theory and Combinatorics Laboratory,Institute of Systems Science,

Academy of Mathematics and System Sciences,Chinese Academy of Sciences,100080Beijing,PR China Received5March2003;received in revised form29December2003;accepted21January2004

Abstract

We investigate structural properties of planar graphs without triangles or without4-cycles,and show that every triangle-free planar graph G is edge-( (G)+1)-choosable and that everyplanar graph with (G)=5and without 4-cycles is also edge-( (G)+1)-choosable.

Keywords:Planar graph;Cycle;Edge choosability

1.Introduction

All graphs considered in this paper are?nite,loopless and without multiple edges.Let G be a plane graph.V(G),E(G) and F(G)shall denote the set of vertices,edges and faces of G,respectively.We say two vertices u and v are adjacent if there is an edge in G joining them;the edge is denoted by uv∈E(G).N G(v)(or N(v))denotes the set of vertices adjacent to v in G.The degree of v,written as d G(v),or simply d(v),is the number of vertices in N G(v).We denote by (G)and (G)the minimum and maximum degrees of vertices of G,respectively.For a face f∈F(G),let V(f)be the set of vertices on the boundaryof f.The degree of f,denoted by (f),means the number of edges on the boundaryof f,where each cut-edge is counted twice.A face f is called simple if the boundaryof f is a cycle.We say v is incident with f,or f is incident with v if v∈V(f).A vertex v is called a k-vertex(or k+-vertex)if d(v)=k(or d(v)?k).We de?ne k-face and k+-face similarly.Obviously,each k-face for36k65is a simple face when (G)?2.A triangle of a graph G is synonymous with a cycle of length3.Let T(v)and Q(v)denote the set of3-and4-faces that are incident with the vertex v,respectively.

An edge-k-coloring of G is a mapping from E(G)to the set of colors{1;2;:::;k}such that (x)= (y)for any adjacent edges x and y of G.The graph is edge-k-colorable if it has an edge-k-coloring.The chromatic index (G)is the smallest integer k such that G is edge-k-colorable.The mapping L is said to be an edge assignment for a graph G if it assigns a list L(e)of possible colors to each edge e of G.If G has some edge-k-coloring such that (e)∈L(e)for all edges e,then we saythat G is edge-L-colorable or is an edge-L-coloring of G.We call G is edge-k-choosable if it is edge-L-colorable for everyedge assignment L satisfying|L(e)|?k for all edges e.The list chromatic index l(G) of G is the smallest integer k such that G is edge-k-choosable.

The following conjecture is well-known on edge choosability.

Conjecture1.1.If G is a multigraph,then l(G)= (G).

?Corresponding author.Tel.:+86-108-268-2022;fax:+86-106-263-3766.

E-mail addresses:zhangli@https://www.wendangku.net/doc/7218814470.html,(L.Zhang),baoyin@https://www.wendangku.net/doc/7218814470.html,(B.Wu).

doi:10.1016/j.disc.2004.01.001

290L.Zhang,B.Wu /Discrete Mathematics 283(2004)289–293

This conjecture has been proved for a few special cases,such as bipartite multigraphs [3],complete graphs of odd order [4],multicircuits [11],line-perfect multigraphs [8],and planar graphs with (G )?12[2].Vizing (see [7])proposed a weaker conjecture as following.

Conjecture 1.2.Everygraph G is edge-( (G )+1)-choosable.

An earlier result of Harris [5]shows that l (G )62 (G )?2if G is a graph with (G )?3.This implies Conjecture 1.2for the case (G )=3.Juvan et al.[6]settled the case of (G )=4.For some special cases such as complete graphs [4],graphs with girth at least 8 (G )(ln (G )+1:1)[7],and planar graphs with (G )?9[1],Conjecture 1.2has also been con?rmed.Wang and Lih [9]proved the conjecture for everyplanar graph G with (G )=5and without 6-cycles.Also,in [10]the same authors proved that everyplanar graph G without 5-cycles is edge-( (G )+1)-choosable.In this paper,we will show that Conjecture 1.2holds for triangle-free planar graphs,and planar graphs with (G )=5and without 4-cycles.

2.Structure of plane graphs without some small cycles

First,we give some additional symbols and concepts that will be used later.Let G be a plane graph.De?ne a weight function w on elements of V (G )∪F (G )byletting w (v )=2d (v )?6for v ∈V (G )and w (f )= (f )?6for f ∈F (G ).Applying Euler’s formula |V (G )|?|E (G )|+|F (G )|=2and the handshaking lemmas for vertices and faces for a plane graph,we have

x ∈V (G )∪F (G )w (x )= v ∈V (G )(2d (v )?6)+ f ∈F (G )

( (f )?6)=?12:

We call w the normal weight .In the proofs of Lemmata 2.1–2.3below,we will obtain another weight function w by transferring the normal weights of vertices to their incident faces.For v ∈V (G )and f ∈F (G ),let z (v;f )be the amount of weights that transferred from v to f .

Lemma 2.1.Let G be a triangle-free plane graph with (G )?5.If d (x )+d (y )? (G )+3for every edge xy ∈E (G ),then (G )=5and G contains a 4-face incident with two 3-vertices and two 5-vertices .

Proof.Suppose G is a triangle-free plane graph such that (G )?5and d (x )+d (y )? (G )+3for everyedge xy ∈E (G ).It follows that (G )?3,and for anyedge uv ∈E (G ),if d (u )=3,then d (v )= (G ).Let w be the normal weight of G .Then w (v )?0for anyvertex v and w (f )?0for any6+-face f .We obtain the new weight function w according to the following rule.

Rule.Transfer w (v )=d (v )from each vertex v to every face f incident with v .

Thus w (v )?0for each vertex v ∈V (G )and for a simple face f ,w (f )=w (f )+ v ∈V (f )w (v )=d (v ).Since we discharge weights from one element to another,the sum of total weights is kept ?xed during the discharging.Thus x ∈V (G )∪F (G )w (x )=?12,which implies that there must be a 4-or 5-face f in G such that w (f )?0.Let f ?be

such a face.Note that for a vertex v ∈V (f ),z (v;f )=w (v )=d (v )=(2d (v )?6)=d (v )?12when d (v )?4.This im-plies that f ?is incident with some 3-vertices.Let v 1∈V (f ?)be a 3-vertex,and v 2and v 3be the two vertices in N (v 1)∩V (f ?).As we have seen before,v 2and v 3are (G )-vertices.Thus we shall conclude that f ?must be a 4-face incident with two 3-vertices and two 5-vertices simplybychecking that w (f ?)?0if f ?satis?es anyof following cases:Case 1: (G )?6.Since w (v )=d (v )=(2d (v )?6)=d (v )?1for d (v )?6,we have z (v i ;f ?)?1for i =2;3,and hence w (f ?)?w (f ?)+1×2?0.Case 2: (G )=5and f ?is a 5-face.We have z (v i ;f ?)?45for i =2;3,and hence w (f ?)?w (f ?)+45×2?0.Case 3: (G )=5and f ?is a 4-face with onlyone 3-vertex.We have z (v i ;f ?)?45for i =2;3.Let v 4∈V (f ?)be the fourth vertex except for v 1;v 2and v 3,then z (v 4;f ?)?12,and so w (f ?)?w (f ?)+45×2+12

?0.Lemma 2.2.Let G be a planar graph with (G )?6.If G does not contain 4-cycles ,then there is an edge xy ∈E (G )such that d (x )+d (y )6 (G )+2.

L.Zhang,B.Wu /Discrete Mathematics 283(2004)289–293291

Fig.1.

Proof.Suppose there is a plane graph G without 4-cycles such that (G )?6and d (x )+d (y )? (G )+3for each edge xy ∈E (G ).Then, (G )?3and if one end vertex of an edge has degree 3,then the other must have the maximum degree (G ).Let w be the normal weight of G .We obtain a new weight function w bydischarging some weights from vertices of G to its incident faces.It is done bythe following rule.

Rule.From each 4+-vertex ,transfer 13to each of its incident 5-faces ,nd then divide the rema iningweig hts to its incident 3-faces .Since we discharge weights from one element to another,the sum of total weights is kept ?xed during the discharging,thus x ∈V (G )∪F (G )w (x )=?12.On the other hand,we will get a contradiction byshowing that w (x )?0for any x ∈V (G )∪F (G ).Bythe discharging rule,it is easyto see that w (x )?0for anyvertex and 6+-face.Let f be a face with (f )∈{3;5}.We consider the following cases.Case 1: (f )=5.If there is no 3-vertex in V (f ),then bythe rule,z (v;f )?13for anyvertex v ∈V (f ).Thus w (f )?w (f )+13×5?0.If there exists a 3-vertex v ∈V (f ),then there are at most two 3-vertices in V (f )since d (x )+d (y )? (G )+3?9for all xy ∈E (G ).We have w (f )?w (f )+13×3?0.Case 2: (f )=3.Let v ∈V (f )be a 4+-vertex.Since G contains no 4-cycles,no two triangles share with one common edge.Therefore,|T (v )|612d (v )and there are at most d (v )?|T (v )|5-faces incident with v .Hence bythe rule,we have z (v;f )?[2d (v )?6?13(d (v )?|T (v )|)]=|T (v )|?[4d (v )?12?d (v )=3]=d (v )?113?12=d (v ).Denote V (f )={v 1;v 2;v 3}.If there is a 3-vertex in V (f ),say v 1,then d (v 2)=d (v 3)= (G ).Moreover,z (v i ;f )?113?12=d (v i )?53since (G )?6for i =2;3.So we have w (f )?w (f )+53×2?0.Now assume that there is no 3-vertex in V (f )and d (v 1)6d (v 2)6d (v 3).Since d (x )+d (y )? (G )+3?9for everyedge xy ∈E (G ),there are at least two 5+-vertices in V (f ).Thus d (v 3)?d (v 2)?5and d (v 1)?4.Since z (v i ;f )?113?12=d (v i ),we have z (v 1;f )?23and z (v i ;f )?1915for i =2;3.Therefore,w (f )?w (f )+23+1915×2?0.So there exists an edge xy ∈E (G )such that d (x )+d (y )6 (G )+2.

From Fig.1,we can see that the result of Lemma 2.2does not hold for the case of (G )=5.In fact,it is a graph with (G )=5and without 4-cycles such that d (x )+d (y )?8for anyedge xy ∈E (G ).However,we can prove the following result.

Lemma 2.3.Let G be a planar graph with (G )=5.If G does not contain 4-cycles ,then there is an edge xy ∈E (G )such that d (x )+d (y )68.

292L.Zhang,B.Wu /Discrete Mathematics 283(2004)289–293

Proof.Suppose there is a plane graph G with (G )=5and without 4-cycles such that d (x )+d (y )?9for each edge xy ∈E (G ),then (G )?4.Let w be the normal weight of G .We will obtain a new weight w bydischarging some weights from vertices of G to their incident faces.

Rule.Transfer 1from every vertex to each of its incident 3-fa ces a nd then divide the rema iningweig hts to its incident 5-faces .

Next,we will check that w (x )?0for anyelement x ∈V (G )∪F (G ).Note that w (v )?2and |T (v )|62for every v ∈V (G )since 46d (v )65and no two triangles share with one common edge.This implies w (v )?0for each v ∈V (G ).It is obvious that w (f )=w (f )?0for a 6+-face f ,and w (f )=0for a 3-face f .Now let f be a 5-face.Since d (x )+d (y )?9for everyedge xy ∈E (G ),no two 4-vertices are adjacent in G .Hence there are at least three 5-vertices in V (f ),and we have w (f )?w (f )+3×23=1?0.However,?12= x ∈V (G )∪F (G )w (x )= x ∈V (G )∪F (G )w (x )?0,a contradiction.So there must be an edge xy ∈E (G )such that d (x )+d (y )68in G .

Corollary 2.4.Let G be a planar graph with (G )?6.If d (x )+d (y )? (G )+3for each edge xy ∈E (G ),then G contains a triangle .

Proof.It is immediate from Lemma 2.1.

3.Application to edge choosability of graphs

We will use the following results in the proofs of Theorems 3.1and 3.2.Let G be a connected graph (not necessarily planar).It is well-known that G is edge-( (G )+1)-choosable for (G )62and in particular is edge-2-choosable if G is an even cycle.From the results of [5,6],G is edge-( (G )+1)-choosable if (G )=3or 4.

Theorem 3.1.Every triangle-free planar graph G is edge -( (G )+1)-choosable .

Proof.We onlyneed to prove the theorem for (G )?5.Byinduction on |E (G )|.The theorem holds triviallyfor graphs G with |E (G )|63.Let L be an edge assignment of G such that |L (e )|= (G )+1for each e ∈E (G ).If there exists an edge xy ∈E (G )such that d (x )+d (y )6 (G )+2,then G ?xy has an edge-L -coloring .We can color xy with some color from L (xy )that was not used by on the edges adjacent to xy .So now we assume that d (x )+d (y )? (G )+3for each edge xy ∈E (G ).This implies that G contains a 4-cycle C incident with two 3-vertices and two 5-vertices byLemma 2.1.Since no two 3-vertices are adjacent in G ,let C =v 1v 2v 3v 4v 1be a 4-cycle of G with d (v 1)=d (v 3)=3;d (v 2)=d (v 4)=5.Then G =G \E (C )admits an edge-list coloring with edge assignment L restricted to G .For all v i v i +1∈E (C ),let L ?(v i v i +1)=L (v i v i +1)\{ (e )|e ∈E (G )is incident with v i or v i +1},where i =1;2;3;4and i +1is taken modulo 4.Thus |L ?(v i v i +1)|?2for all v i v i +1∈E (C ),and then the 4-cycle C admits an edge-list coloring with edge assignment L ?.We obtain an edge-list coloring of G with edge assignment L .

Theorem 3.2.If G is a planar graph without 4-cycles ,then G is edge -t -choosable ,where t =7if (G )=5,otherwise t = (G )+1.

Proof.We proceed byinduction on |E (G )|.The result is trivial for graphs G with |E (G )|63.Now we assume that G is a plane graph without 4-cycles and (G )?5.Let L be an edge assignment of G such that |L (e )|=t for each e ∈E (G )(i.e.t =7if (G )=5,otherwise t = (G )+1).First,suppose (G )=5.ByLemma 2.3,there is an edge xy ∈E (G )such that d (x )+d (y )68.The induction hypothesis implies that G ?xy has an edge-L -coloring .Since xy is adjacent to at most 6edges in G and |L (xy )|=7,we can color xy with some color from L (xy )that was not used by on the edges adjacent to xy .Now,suppose (G )?6.ByLemma 2.2,there exists an edge xy ∈E (G )such that d (x )+d (y )6 (G )+2.Also,G ?xy has an edge-L -coloring .We can color xy with some color from L (xy )that was not used by on the edges adjacent to xy .

It seems that the method of discharging weights does not work for proofs of edge choosabilityfor planar graphs without cycles of length 4,or 6when (G )=5.

L.Zhang,B.Wu/Discrete Mathematics283(2004)289–293293 Acknowledgements

We would like to express our gratitude to both referees for their careful reading and helpful comments.In particular, we are indebted to one of them for pointing out a aw in the proof of Theorem3.2.

References

[1]O.V.Borodin,An extension of Kotzig’s theorem and the list edge coloring of plane graphs,Mat.Zametki48(1990)22–28

(in Russian).

[2]O.V.Borodin,A.V.Kostochka,D.R.Woodall,List edge and list total coloring of multigraphs,https://www.wendangku.net/doc/7218814470.html,bin.TheorySer.B71(1997)

184–204.

[3]F.Galvin,The list chromatic index of a bipartite multigraph,https://www.wendangku.net/doc/7218814470.html,bin.TheorySer.B63(1995)153–158.

[4]R.H a ggkvist,J.Janssen,New bounds on the list-chromatic index of the complete graph and other simple graphs,Combin.Probab.

Comput.6(1997)295–313.

[5]A.J.Harris,Problems and conjectures in extremal graph theory,Ph.D.Dissertation,Cambridge University,UK,1984.

[6]M.Juvan,B.Mohar,R. Skrekovski,Graphs of degree4are5-edge-choosable,J.Graph Theory32(1999)250–262.

[7]A.V.Kostochka,List edge chromatic number of graphs with large girth,Discrete Math.101(1992)189–201.

[8]D.Peterson,D.R.Woodall,Edge-choosabilityin line-perfect multigraphs,Discrete Math.202(1999)191–199.

[9]W.Wang,K.W.Lih,Structural properties and edge choosabilityof planar graphs without6-cy cles,https://www.wendangku.net/doc/7218814470.html,put.10

(2001)267–276.

[10]W.Wang,K.W.Lih,Choosabilityand edge choosabilityof planar graphs without?ve cy cles,Appl.Math.Lett.15(2002)

561–565.

[11]D.R.Woodall,Edge-choosabilityof multicircuits,Discrete Math.202(1999)271–277.

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英语专业四级note writing讲解

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红米NOTE

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商务英语note

Unit1 Text A Translation 1.After months of researching Northwestern on the Web and grilling friends,teachers and advisers who had gone there,Maxine pinned her hopes on getting accepted. 经过数月在网上搜集并研究西北大学和仔细研究询问到西北大学的朋友，老师和咨询顾问，玛克辛最终希望自己被西北大学录取。 2.For students like Maxine who are applying to college for next fall,that dream is turning out to be frustratingly unobtainable. It turns out the odds of getting into a selective college have never been worse. 对于像玛克辛一样正在申请秋季入学的学生来说，他们会沮丧的发现这一梦想难以实现，考入一所知名院校的机会从未如此渺茫。 3.But when you see a kid collapse with grief because they didn’t get in,well,that’s not fun. 但是当你看到一个孩子因为被录取感到伤心而一蹶不振，那可不是闹着玩的。 4.College counselors say that as schools get choosier,parents have grown more resigned to the realities of kids’ prospects. 大学咨询人员说由于学校对录取越来越慎重，家长已经比过去更能平静地对待孩子被大学录取几率渺茫的事实了。 5.College admissions offers are split. On the one hand,they say they don’t like being forced to reject so many worthy kids. On the other hand,they’re enjoying--and profiting from--the attention. 校方招生主管意见不一。一方面，他们说他们不愿意被迫拒绝这些优秀的孩子。另一方面，他们正在享受这种关注的乐趣，并从中获利。 6.At some colleges the bumper crop of applications is causing crowd-control problems. For years Rutgers University has run a private bus to ferry prospective students and their parents around its sprawling New Brunswick,N.J.,campus. 在一些院校，申请者激增引发了校园过度拥挤的问题。多年来，罗格斯大学为正在扩大的新布朗斯维克校区增开一趟专用车，接送未来的学生和家长。 7.By 2015 the number of high-school graduates will begin to drop back out of the stratosphere. But admissions directors are ready worrying about the shrinking pool of future applicants,especially the sliver of those who can afford to foot the $40,000 annual tab. 到2015年，高中毕业生的数量将开始回落。但是招生主管们已经开始担忧申请者数量缩减的问题，尤其是为数不多的每年有能力支付4万美元费用的那部分申请者。 8.”I know I’m one of many,but that doesn’t mean I’m not smart and driven and ready to be a committed student.” “我知道我是众多未被录取的申请者中的一位，但这并不说明我不优秀，我不努力，我不是一名上进的学生。

解决红米note 用USB连接电脑所遇到的MTP驱动问题

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1.开始-设置-控制版面-管理工具-计算机管理-设备管理器右击MTP-属性-详细信息 USB\VID_XXXX&PID_XXXX 记下VID和PID后面的四位XXXX 2.右键我的电脑-资源管理器找到c:\windows\inf\wpdmtp.inf打开，如果找不到，应该是隐藏了。这要到控制版面-文件夹选项-查看-选显示隐藏文件（给大家一个小窍门，直接复制c:\windows\inf\wpdmtp.inf到开始的运行内直接运行就可以调出）找到 [Generic.NTx86] %GenericMTP.DeviceDesc%=MTP, USB\MS_COMP_MTP %GenericMTP.DeviceDesc%=MTP,USB\VID_xxxx&PID_xxxx&MI_00 [Generic.NTamd64] %GenericMTP.DeviceDesc%=MTP, USB\MS_COMP_MTP

高考英语满分作文：Note(便条)

高考英语满分作文：Note(便条) Dear Alice. I wonder if you eould lend me your Chinese-English dictionary. I will return it three days later. Now I am translating an important Chinese article into English. However, I often meet some Chinese words which I don't know how to say in English. So I have to turn to the Chinese-English dietionary for help from time to time. But mine is lost. I will take good care of your dictionary. I will definitely not damage it. Thank you very much! Jenny 亲爱的艾丽丝：我想知道你能否把你的汉英词典借给我，三天后还给你。现在我正在把一篇重要的中文文章翻译成英文。不过我经常遇到一些不知如何用英语表达的词，所以我必须时不时地求助于汉英词典，但是我的丢了。我会好好爱护你的词典，绝不损坏。非常感谢! 珍妮 5月15日 May 15th Dear Alice, Would you please lend me your Chinese-English dictionary? I will give it back three days later. Now I am translating an important Chinese article into English. In the article I often find Chinese words which I cannot translate into English, so I often need a Chinese-English dictionary' But I

三星Galaxy note2 N7100 Odin3刷机教程

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红米NOTE 移动版精简列表

红米NOTE 移动版精简列表部分精简列表：以下程序删除并不会影响系统 1 AirkanPhoneService.apk 2 BaiduNetworkLocation.apk 3 BasicDreams.apk 4 BugReport.apk 5 CertInstaller.apk 6 cit.apk 7 DrmProvider.apk 8 Email.apk 9 Exchange2.apk 10 Galaxy4.apk 11 GameCenter.apk 12 GameCenterSDKService.apk 13 HoloSpiralWallpaper.apk 14 HTMLViewer.apk 15 jjhome.apk 16 jjmms.apk 17 LiveWallpapers.apk 18 MagicSmokeWallpapers.apk

19 MiuiVideo.apk 20 NoiseField.apk 21 Paymentservice.apk 22 PhaseBeam.apk 23 SharedStorageBackup.apk 24 SuperMarket.apk 25 UserbookProvider.apk 26 UserDictionaryProvider.apk 27 VisualizationWallpapers.apk 28 Voiceassist.apk 29 WAPPushManager.apk 极致精简注：极致精简版是全功能版的深度精简版本，在全功能的基础上精简了大量很少用到的APP 和冗余，请认真查看极致精简版的精简列表，以便了解哪些功能被剔除。 1 AdupsFota.apk 2 AdupsFotaReboot.apk 3 ApplicationsProvider.apk 4 Browser.apk 5 Calculater.apk 6 Calendar.apk 7 CalendarProvider.apk 8 cit.apk

三星GALAXY note2(N7100)刷机教程详细图文解说

注意刷机有风险本人只在自己的机器上测试,刷机和ROOT带来的一切问题与本人无关三星Note2线刷教程: 刷机准备工具: 1 三星的KIES(目的是此软件有三星最新产品的驱动,安装完毕后请重启一次电脑) 2 odin3刷机工具 3 ROM(下载好后如压缩包后缀为.ZIP 请解压出文件,如解压后的文件后缀为.tar.md5 那么请重命名给.md5这个去掉,得到.tar的文件.) 三个文件的下载地址在最下面开始三星Note2刷机的步骤: 1.备份好手机里的重要资料(切记备份一下重要资料,刷机后双W会丢失手机里的数据) 2.手机进入设置-开发者选项-USB调试(勾选上) 3.手机关机，同时按住（音量下键+HOME键+电源键）5秒左右，会出现下图样子

看到上图后按下音量上键，然后会出现安卓小绿人,如下图

这时连接电脑(请把数据线插入电脑主机的后端USB 插孔上,前端USB插孔很有可能供电不足)。 4.在电脑端打开Odin软件,odin软件会识别手机识别成功后会在ID：COM处显示黄色如下图

5.选择软件中的PDA ,找到您下载好的ROM(.tar的那个)然后点打开 6.选择start(开始) 7.电脑端软件左上角出现绿色进度条为刷机中,手机端也会有进度条如下图

可以点根烟喝杯水了, 出现下图中的PASS即表示刷机完成

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确认三星n7102救砖此时页面显示部分手机品牌，点击“Samsung”按钮，页面出现三星系列手机，在搜索框内输入手机型号，如“7102”，点击筛选出的“Galaxy Note2(n7102)”手机图案。之后，弹出确认是否要给三星n7102救砖对话框，阅读完后选择“确定”。

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进行ROOT 点击“更多工具”，选择“ROOT大师"对红米Note移动版一键ROOT ，等待ROOT成功后自动重启。数据备份点击“更多工具”，选择“备份大师"对你的手机进行数据备份。

搜索红米Note移动版的刷机包选择红米Note移动版的刷机包或者是点击刷机大师里面的ROM基地，然后搜索红米Note 移动版，点击进去就可以见到红米Note移动版的ROM包。选择红米Note移动版的YunOS刷机包在红米Note移动版的刷机包的列表里面，你可以看到有种类繁多的第三方ROM系统，选择你要下载YunOS刷机包。一键刷机准备好ROM，我们就可以开始一键刷机了，刷机开始之前中刷机大师会对手机和对刷机包进行检查，点击“浏览”选中刚才下载好的ROM，别忘了按照提示备份好联系人、短信和应用哦。