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1.
Xuding Zhu 《Journal of Graph Theory》2005,48(3):210-218
This paper discusses the circular version of list coloring of graphs. We give two definitions of the circular list chromatic number (or circular choosability) χc, l(G) of a graph G and prove that they are equivalent. Then we prove that for any graph G, χc, l(G) ≥ χl(G) ? 1. Examples are given to show that this bound is sharp in the sense that for any ? 0, there is a graph G with χc, l(G) > χl(G) ? 1 + ?. It is also proved that k‐degenerate graphs G have χc, l(G) ≤ 2k. This bound is also sharp: for each ? < 0, there is a k‐degenerate graph G with χc, l(G) ≥ 2k ? ?. This shows that χc, l(G) could be arbitrarily larger than χl(G). Finally we prove that if G has maximum degree k, then χc, l(G) ≤ k + 1. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 210–218, 2005 相似文献
2.
This note proves that the game chromatic number of an outerplanar graph is at most 7. This improves the previous known upper bound of the game chromatic number of outerplanar graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 67–70, 1999 相似文献
3.
《Journal of Graph Theory》2018,87(1):18-34
A proper vertex coloring of a graph G is achromatic (respectively harmonious) if every two colors appear together on at least one (resp. at most one) edge. The largest (resp. the smallest) number of colors in an achromatic (resp. a harmonious) coloring of G is called the achromatic (resp. harmonious chromatic) number of G and denoted by (resp. ). For a finite set of positive integers and a positive integer n, a circulant graph, denoted by , is an undirected graph on the set of vertices that has an edge if and only if either or is a member of (where substraction is computed modulo n). For any fixed set , we show that is asymptotically equal to , with the error term . We also prove that is asymptotically equal to , with the error term . As corollaries, we get results that improve, for a fixed k, the previously best estimations on the lengths of a shortest k‐radius sequence over an n‐ary alphabet (i.e., a sequence in which any two distinct elements of the alphabet occur within distance k of each other) and a longest packing k‐radius sequence over an n‐ary alphabet (which is a dual counterpart of a k‐radius sequence). 相似文献
4.
Xuding Zhu 《Journal of Graph Theory》2008,59(4):261-278
This article proves the following result: Let G and G′ be graphs of orders n and n′, respectively. Let G* be obtained from G by adding to each vertex a set of n′ degree 1 neighbors. If G* has game coloring number m and G′ has acyclic chromatic number k, then the Cartesian product G□G′ has game chromatic number at most k(k + m ? 1). As a consequence, the Cartesian product of two forests has game chromatic number at most 10, and the Cartesian product of two planar graphs has game chromatic number at most 105. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 261–278, 2008 相似文献
5.
Stephan Dominique Andres Winfried Hochstättler Christiane Schallück 《Discrete Applied Mathematics》2011,159(16):1660-1665
We prove that the game chromatic index of n-wheels is n for n≥6. 相似文献
7.
The circular chromatic index of a graph G, written , is the minimum r permitting a function such that whenever e and are incident. Let □ , where □ denotes Cartesian product and H is an ‐regular graph of odd order, with (thus, G is s‐regular). We prove that , where is the minimum, over all bases of the cycle space of H, of the maximum length of a cycle in the basis. When and m is large, the lower bound is sharp. In particular, if , then □ , independent of m. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 7–18, 2008 相似文献
8.
A. V. Pyatkin 《Journal of Graph Theory》2002,41(4):286-291
P. Erd?s conjectured in [2] that r‐regular 4‐critical graphs exist for every r ≥ 3 and noted that no such graphs are known for r ≥ 6. This article contains the first example of a 6‐regular 4‐critical graph. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 286–291, 2002 相似文献
9.
We prove that the strong chromatic index of a 2‐degenerate graph is linear in the maximum degree Δ. This includes the class of all chordless graphs (graphs in which every cycle is induced) which in turn includes graphs where the cycle lengths are multiples of four, and settles a problem by Faudree et al. (Ars Combin 29(B) (1990), 205–211). © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 119–126, 2013 相似文献
10.
Mycielski图的循环色数 总被引：1，自引：0，他引：1
通过引入一类点集划分的概念,研究了Mylielski图循环染色的性质,证明了当完全图的点数足够大时,它的Mycielski图的循环色数与其点色数相等. 相似文献
11.
Wenjie He Xiaoling Hou Ko‐Wei Lih Jiating Shao Weifan Wang Xuding Zhu 《Journal of Graph Theory》2002,41(4):307-317
Let G be a planar graph and let g(G) and Δ(G) be its girth and maximum degree, respectively. We show that G has an edge‐partition into a forest and a subgraph H so that (i) Δ(H) ≤ 4 if g(G) ≥ 5; (ii) Δ(H) ≤ 2 if g(G) ≥ 7; (iii) Δ(H)≤ 1 if g(G) ≥ 11; (iv) Δ(H) ≤ 7 if G does not contain 4‐cycles (though it may contain 3‐cycles). These results are applied to find the following upper bounds for the game coloring number colg(G) of a planar graph G: (i) colg(G) ≤ 8 if g(G) ≥ 5; (ii) colg(G)≤ 6 if g(G) ≥ 7; (iii) colg(G) ≤ 5 if g(G) ≥ 11; (iv) colg(G) ≤ 11 if G does not contain 4‐cycles (though it may contain 3‐cycles). © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 307–317, 2002 相似文献
12.
Suppose G is a graph and k,d are integers. The (k,d)-relaxed colouring game on G is a game played by two players, Alice and Bob, who take turns colouring the vertices of G with legal colours from a set X of k colours. Here a colour i is legal for an uncoloured vertex x if after colouring x with colour i, the subgraph induced by vertices of colour i has maximum degree at most d. Alice’s goal is to have all the vertices coloured, and Bob’s goal is the opposite: to have an uncoloured vertex without a legal colour. The d-relaxed game chromatic number of G, denoted by , is the least number k so that when playing the (k,d)-relaxed colouring game on G, Alice has a winning strategy. This paper proves that if G is an outerplanar graph, then for d≥6. 相似文献
13.
14.
A.V. Pyatkin 《Journal of Graph Theory》2001,37(4):243-246
This note contains an example of a 4‐chromatic graph which admits a vertex partition into three parts such that the union of every two of them induces a forest. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 243–246, 2001 相似文献
15.
De Ming Li 《数学学报(英文版)》2002,18(1):173-180
The notion of the star chromatic number of a graph is a generalization of the chromatic number. In this paper, we calculate
the star chromatic numbers of three infinite families of planar graphs. The first two families are derived from a 3-or 5-wheel
by subdivisions, their star chromatic numbers being 2+2/(2n + 1), 2+3/(3n + 1), and 2+3(3n−1), respectively. The third family of planar graphs are derived from n odd wheels by Hajos construction with star chromatic numbers 3 + 1/n, which is a generalization of one result of Gao et al.
Received September 21, 1998, Accepted April 9, 2001. 相似文献
16.
H. A. Kierstead 《Journal of Graph Theory》2005,48(3):169-185
We introduce the (a,b)‐coloring game, an asymmetric version of the coloring game played by two players Alice and Bob on a finite graph, which differs from the standard version in that, in each turn, Alice colors a vertices and Bob colors b vertices. We also introduce a related game, the (a,b)‐marking game. We analyze these games and determine the (a,b)‐chromatic numbers and (a,b)‐coloring numbers for the class of forests and all values of a and b. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 169–185, 2005 相似文献
17.
本文介绍了边对策着色,讨论了图G的边对策着色的性质.对几种特殊图类进行了讨论,分别确定链图,圈图及与圈有关的图,扇图,Petersen图的边对策色数. 相似文献
18.
In 1960, Dirac posed the conjecture that r‐connected 4‐critical graphs exist for every r ≥ 3. In 1989, Erd?s conjectured that for every r ≥ 3 there exist r‐regular 4‐critical graphs. In this paper, a technique of constructing r‐regular r‐connected vertex‐transitive 4‐critical graphs for even r ≥ 4 is presented. Such graphs are found for r = 6, 8, 10. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 103–130, 2004 相似文献
19.
赋权图的区间染色的定义与赋权图的圆染色的定义非常类型,唯一的区别就是将Ｇ的顶点对应圆周上的孤换为Ｇ的顶点对应区间上的子区间,讨论了赋权的圆染色与区染色的关系。 相似文献
20.
图的星色数是通常色数概念的推广.本文求出了几类由轮图导出的平面图的星色数.前两类是由3-或5-轮图经细分等构造出的,其星色数分别为2+2/(2n+1),2+3/(3n+1)和2+3/(3n-1).第三类平面图是由n-轮图经过Hajos构造得到的,其星色数为3+1/n.本类图的星色数结果推广了已有结论. 相似文献