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《数学的实践与认识》2015,(23)
对图G的一个正常边染色,如果图G的任何一个圈至少染三种颜色,则称这个染色为无圈边染色.若L为图G的一个边列表,对图G的一个无圈边染色φ,如果对任意e∈E(G)都有ф(e)∈L(e),则称ф为无圈L-边染色.用a′_(list)(G)表示图G的无圈列表边色数.证明若图G是一个平面图,且它的最大度△≥8,围长g(G)≥6,则a′_(list)(G)=△. 相似文献
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对于图G=(V(G),E(G)),如果一个映射φ:E(G)→{1,2,…,k},使得G中任意相邻的两边e1,e2满足φ(e1)≠φ(e2),并且G中不含有双色圈,则称φ为G的一个无圈边染色.对于给定的列表分配L={L(e)|e∈E(G)},如果存在图G的一个无圈边染色φ,使得对于任意边e∈E(G),均有φ(e)∈L(e),则称染色φ为G的一个无圈L-边染色.如果对于任意的列表分配L,当对所有的边e∈E(G)满足|L(e)|≥k时,图G均存在无圈L-边染色,那么称G是无圈k-边可选的.使图G无圈k-边可选的最小的正整数k,称为G的无圈列表边色数,用a’l(G)表示.本文证明了对于最大度△≤4的连通图G,如果|E(G)|≤2|V(G)|-1,则a’l(G)≤6,扩展了Basavaraju和Chandran文[J.Graph Theory,2009,61(3):192-209]的结果. 相似文献
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图的(列表)动态染色模型可用于解决信道分配中的一些关键问题,是图论和理论计算机科学领域的一个重要的研究方向.Kim和Park (2011)给出了任何最大平均度小于8/3的图的列表动态色数至多为4的证明.然而,由于具有5个顶点的圈C5的最大平均度为2且列表动态色数为5,因此Kim和Park的上述结论是错误的.基于此,本文证明了任何最大平均度小于8/3的普通图(每个连通分支都不与C5同构的图)的列表动态色数至多为4,且该上界4是最优的,从而对Kim和Park的结果进行了修正.与此同时,本文证明了如果图G是系列平行图,则当其是普通图时,其列表动态色数至多为4,且该上界4是最优的,当其不是普通图时,其列表动态色数恰好为5,从而将Song等人(2014)的结果“任何系列平行图的列表动态色数至多为6”进行了改进. 相似文献
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图$G$的正常边染色称为无圈的, 如果图$G$中不含2-色圈, 图$G$的无圈边色数用$a''(G)$表示, 是使图$G$存在正常无圈边染色所需要的最少颜色数. Alon等人猜想: 对简单图$G$, 有$a''(G)\leq{\Delta(G)+2}$. 设图$G$是围长为$g(G)$的平面图, 本文证明了: 如果$g(G)\geq3$, 则$a''(G)\leq\max\{2\Delta(G)-2,\Delta(G)+22\}$; 如果 $g(G)\geq5$, 则$a''(G)\leq{\Delta(G)+2}$; 如果$g(G)\geq7$, 则$a''(G)\leq{\Delta(G)+1}$; 如果$g(G)\geq16$并且$\Delta(G)\geq3$, 则$a''(G)=\Delta(G)$; 对系列平行图$G$, 有$a''(G)\leq{\Delta(G)+1}$. 相似文献
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如果一个图G存在一个k-列表安排使得G具有一个唯一列表染色,则称 G是唯一列表可染色图,简称UkLC图.我们称图G具有M(k)性质当且仅当G不 是UkLC图.本文在借鉴θr,s,t-图概念的基础上引入θr,s,t-图的定义,并证明:除了 r=s=t=2以外,θr,s,t-图都是U2LC图.利用如上结果我们给出M.Mahdian and E.S.Mahmoodian对U2LC图所作特征化的一个简单证明. 相似文献
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Acta Mathematicae Applicatae Sinica, English Series - A k-coloring of a graph G is a mapping c: V(G) → {1, 2, ?, k}. The coloring c is called injective if any two vertices have a common... 相似文献
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Adam Berliner Ulrike Bostelmann Richard A. Brualdi Louis Deaett 《Graphs and Combinatorics》2006,22(2):173-183
Let G=(V,E) be a graph with n vertices and e edges. The sum choice number of G is the smallest integer p such that there exist list sizes (f(v):v ∈ V) whose sum is p for which G has a proper coloring no matter which color lists of size f(v) are assigned to the vertices v. The sum choice number is bounded above by n+e. If the sum choice number of G equals n+e, then G is sum choice greedy. Complete graphs Kn are sum choice greedy as are trees. Based on a simple, but powerful, lemma we show that a graph each of whose blocks is sum
choice greedy is also sum choice greedy. We also determine the sum choice number of K2,n, and we show that every tree on n vertices can be obtained from Kn by consecutively deleting single edges where all intermediate graphs are sc-greedy. 相似文献
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A graph is f-choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. We characterize f-choosable functions for block graphs (graphs in which each block is a clique, including trees and line graphs of trees). The sum choice number is the minimum over all choosable functions f of the sum of the sizes in f. The sum choice number of any graph is at most the number of vertices plus the number of edges. We show that this bound is tight for block graphs.Acknowledgments. Partially supported by a grant from the Reidler Foundation. The author would like to thank an anonymous referee for useful comments. 相似文献
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A proper edge coloring of a graph is said to be acyclic if any cycle is colored with at least three colors. An edge-list L of a graph G is a mapping that assigns a finite set of positive integers to each edge of G. An acyclic edge coloring ? of G such that for any is called an acyclic L-edge coloring of G. A graph G is said to be acyclically k-edge choosable if it has an acyclic L‐edge coloring for any edge‐list L that satisfies for each edge e. The acyclic list chromatic index is the least integer k such that G is acyclically k‐edge choosable. We develop techniques to obtain bounds for the acyclic list chromatic indices of outerplanar graphs, subcubic graphs, and subdivisions of Halin graphs. 相似文献
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A graph G is equitably k‐choosable if for every k‐list assignment L there exists an L‐coloring of G such that every color class has at most vertices. We prove results toward the conjecture that every graph with maximum degree at most r is equitably ‐choosable. In particular, we confirm the conjecture for and show that every graph with maximum degree at most r and at least r3 vertices is equitably ‐choosable. Our proofs yield polynomial algorithms for corresponding equitable list colorings. 相似文献
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For a graph G, let be the maximum number of vertices of G that can be colored whenever each vertex of G is given t permissible colors. Albertson, Grossman, and Haas conjectured that if G is s‐choosable and , then . In this article, we consider the online version of this conjecture. Let be the maximum number of vertices of G that can be colored online whenever each vertex of G is given t permissible colors online. An analog of the above conjecture is the following: if G is online s‐choosable and then . This article generalizes some results concerning partial list coloring to online partial list coloring. We prove that for any positive integers , . As a consequence, if s is a multiple of t, then . We also prove that if G is online s‐choosable and , then and for any , . 相似文献
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Edge Coloring of Embedded Graphs with Large Girth 总被引:3,自引:0,他引:3
Let G be a simple graph embedded in the surface of Euler characteristic ()0. Denote e(G), and g the edge chromatic number, the maximum degree and the girth of the graph G, respectively. The paper shows that e(G)= if 5 and g4, or 4 and g5, or 3 and g9. In addition, if ()>0, then e(G)= if 3 and g8.
Acknowledgments.The authors would like to thank Dr. C.Q. Zhang for carefully reading several versions of this paper during its preparation and for suggesting several stylistic changes that have improved the overall presentation. 相似文献
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The vertex-arboricity a(G) of a graph G is the minimum number of colors required for a vertex coloring of G such that no cycle is monochromatic. The list vertex-arboricity al(G) is the list-coloring version of this concept. In this paper, we prove that every planar graph G without intersecting 5-cycles has al(G) ≤ 2.This extends a result by Raspaud and Wang [On the vertex-arboricity of planar graphs, European J. Combin.29(2008), 1064-1075] that every planar graph G without 5-cycles has a(G) ≤ 2. 相似文献
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choice number of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). It is shown that the choice number of the random graph G(n, p(n)) is almost surely whenever . A related result for pseudo-random graphs is proved as well. By a special case of this result, the choice number (as well
as the chromatic number) of any graph on n vertices with minimum degree at least in which no two distinct vertices have more than common neighbors is at most .
Received: October 13, 1997 相似文献