共查询到20条相似文献,搜索用时 203 毫秒
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如果图G的一个正常边染色满足相邻点的色集不同,且任意两种颜色所染边数目相差不超过1,则称为均匀邻强边染色,其所用最少染色数称为均匀邻强边色数.本文得到了星、扇和轮的倍图的均匀邻强边色数. 相似文献
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如果图G的一个正常边染色满足相邻点的色集不同,且任意两种颜色所染边数目相差不超过1,则称为均匀邻强边染色,其所用最少染色数称为均匀邻强边色数.本文得到了路、圈、星和扇的Mycielski图的均匀邻强边色数. 相似文献
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如果图G的一个正常边染色满足相邻点的色集不同,且任意两种颜色所染边数相差不超过1,则称为均匀邻强边染色,其所用最少染色数称为均匀邻强边色数.本文得到在m=1,2,3,n≥1和m=n≥4时的均匀邻强边色数. 相似文献
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A b‐coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b‐chromatic number of a graph G is the largest integer k such that G admits a b‐coloring with k colors. A graph is b‐perfect if the b‐chromatic number is equal to the chromatic number for every induced subgraph of G. We prove that a graph is b‐perfect if and only if it does not contain as an induced subgraph a member of a certain list of 22 graphs. This entails the existence of a polynomial‐time recognition algorithm and of a polynomial‐time algorithm for coloring exactly the vertices of every b‐perfect graph. © 2011 Wiley Periodicals, Inc. J Graph Theory 71:95–122, 2012 相似文献
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The weak chromatic number, or clique chromatic number (CCHN) of a graph is the minimum number of colors in a vertex coloring, such that every maximal clique gets at least two colors. The weak chromatic index, or clique chromatic index (CCHI) of a graph is the CCHN of its line graph.Most of the results here are upper bounds for the CCHI, as functions of some other graph parameters, and contrasting with lower bounds in some cases. Algorithmic aspects are also discussed; the main result within this scope (and in the paper) shows that testing whether the CCHI of a graph equals is NP-complete. We deal with the CCHN of the graph itself as well. 相似文献
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王国兴 《数学的实践与认识》2012,42(6):233-236
设G是简单图,图G的一个k-点可区别Ⅵ-全染色(简记为k-VDIVT染色),f是指一个从V(G)∪E(G)到{1,2,…,k}的映射,满足:()uv,uw∈E(G),v≠w,有,f(uv)≠f(uw);()u,V∈V(G),u≠v,有C(u)≠C(v),其中C(u)={f(u)}∪{f(uv)|uv∈E(G)}.数min{k|G有一个k-VDIVT染色}称为图G的点可区别Ⅵ-全色数,记为x_(vt)~(iv)(G).讨论了完全图K_n及完全二部图K_(m,n)的VDIVT色数. 相似文献
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Let G be a simple graph.An IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color.Let C(u) be the set of colors of vertex u and edges incident to u under f.For an IE-total coloring f of G using k colors,if C(u)=C(v) for any two different vertices u and v of V(G),then f is called a k-vertex-distinguishing IE-total-coloring of G,or a k-VDIET coloring of G for short.The minimum number of colors required for a VDIET coloring of G is denoted by χ ie vt (G),and it is called the VDIET chromatic number of G.We will give VDIET chromatic numbers for complete bipartite graph K4,n (n≥4),K n,n (5≤ n ≤ 21) in this article. 相似文献
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《数学季刊》2016,(2):147-154
Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C(x) be the set of colors of vertex x and edges incident to x under f. For an IE-total coloring f of G using k colors, if C(u) 6= C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χievt(G) and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. The VDIET colorings of complete bipartite graphs K8,n are discussed in this paper. Particularly, the VDIET chromatic number of K8,n are obtained. 相似文献
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Keith Edwards 《Journal of Graph Theory》1998,29(4):257-261
A harmonious coloring of a simple graph G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colors in such a coloring. We obtain a new upper bound for the harmonious chromatic number of general graphs. © 1998 John Wiley & Sons, Inc. J Graph Theory 29: 257–261, 1998 相似文献
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Let G be a simple graph of order at least 2.A VE-total-coloring using k colors of a graph G is a mapping f from V (G) E(G) into {1,2,···,k} such that no edge receives the same color as one of its endpoints.Let C(u)={f(u)} {f(uv) | uv ∈ E(G)} be the color-set of u.If C(u)=C(v) for any two vertices u and v of V (G),then f is called a k-vertex-distinguishing VE-total coloring of G or a k-VDVET coloring of G for short.The minimum number of colors required for a VDVET coloring of G is denoted by χ ve vt (G) and it is called the VDVET chromatic number of G.In this paper we get cycle C n,path P n and complete graph K n of their VDVET chromatic numbers and propose a related conjecture. 相似文献
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王国兴 《数学的实践与认识》2014,(21)
图G的正常边染色称为是点可区别的,如果对G的任意两顶点的关联边的颜色构成的集合不同.对图G进行点可区别正常边染色所需要的最少颜色数称为图G的点可区别正常边色数,记为x_s'(G).给出了3阶空图与t阶完全图的联图的点可区别正常边色数. 相似文献
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Let G be a simple graph.An IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color.Let C(u) be the set of colors of vertex u and edges incident to u under f.For an IE-total coloring f of G using k colors,if C(u)=C(v) for any two different vertices u and v of V(G),then f is called a k-vertex-distinguishing IE-total-coloring of G,or a k-VDIET coloring of G for short.The minimum number of colors required for a VDIET coloring of G is denoted by χ ie vt (G),and it is called the VDIET chromatic number of G.We will give VDIET chromatic numbers for complete bipartite graph K4,n (n≥4),K n,n (5≤ n ≤ 21) in this article. 相似文献
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A clique coloring of a graph is a coloring of the vertices so that no maximal clique is monochromatic (ignoring isolated vertices). The smallest number of colors in such a coloring is the clique chromatic number. In this paper, we study the asymptotic behavior of the clique chromatic number of the random graph ??(n,p) for a wide range of edge‐probabilities p = p(n). We see that the typical clique chromatic number, as a function of the average degree, forms an intriguing step function. 相似文献
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For integers k0,r0,a(k,r)-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d,r}diferent colors.The r-hued chromatic number,denoted byχr(G),is the smallest integer k for which a graph G has a(k,r)-coloring.Define a graph G is r-normal,ifχr(G)=χ(G).In this paper,we present two sufcient conditions for a graph to be 3-normal,and the best upper bound of 3-hued chromatic number of a certain families of graphs. 相似文献