共查询到19条相似文献,搜索用时 93 毫秒
1.
广义图K(n,m)的全色数 总被引:1,自引:0,他引:1
1965年,M.Behzad和Vizing分别提出了著名的全着色猜想:即对于简单图G有:XT(G)≤△+2,其中△是图G的最大度.本文确定了完全图Kn的广义图K(n,m)的全色数,并利用它证明了Lm×Kn(m≥3)是第Ⅰ型的. 相似文献
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路与完全图的笛卡尔积图和广义图K(n,m)的关联色数 总被引:4,自引:0,他引:4
Richrd A.Brualdi和J.Quinn Massey在[1]中引入了图的关联着色概念,并且提出了关联着色猜想,即每一个图G都可以用△(G)+2种色正常关联着色.B.Guiduli[2]说明关联着色的概念是I.Algor和N.Alon[3]提出的有向星荫度的一个特殊情况,并证实[1]的关联着色猜想是错的,给出图G的关联色数的一个新的上界是△(G)+O(Log(△G)).[4]确定了某些特殊图类的关联色数.本文给出了路和完全图的笛卡尔积图的关联色数,而且利用此结果又确定了完全图Kn的广义图K(n,m)的关联色数. 相似文献
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完全二部图广义Mycielski图的邻点可区别全色数与邻强边色数 总被引:6,自引:1,他引:5
得到了完全二部图Km,n的广义Mycielski图Ml(Km,n),当(l≥1,n≥m≥2)时的邻点可区别全色数与邻强边色数. 相似文献
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杨随义 《数学的实践与认识》2023,(5):142-152
图G的邻点可区别Ⅰ-全染色是一个满足相邻顶点色集合不同的Ⅰ-全染色,其中任意一点的色集合包含该顶点及其关联边所染的颜色.所需颜色的最小数称为邻点可区别Ⅰ-全色数,记作χati(G).研究了路和圈的广义Mycielski图的邻点可区别Ⅰ-全色数:对于阶数n≥2的路Pn,当n=2,3,4时,有χati(M(Pn))=n+1;否则,χati(M(Pn))=n.对于阶数n≥3的圈Cn,当n=3,4时,有χati(M(Cn))=5;否则,χati(M(Cn))=n. 相似文献
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马刚 《数学的实践与认识》2012,42(9):207-213
研究了一些Mycielski图的点可区别均匀全染色(VDETC),利用构造法给出了路、圈、星和扇的Mycielski图的点可区别均匀全色数,验证了它们满足点可区别均匀全染色猜想(VDETCC). 相似文献
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Let G be a planar graph. The vertex face total chromatic number χ13(G) of G is the least number of colors assigned to V(G)∪F(G) such that no adjacent or incident elements receive the same color. The main results of this paper are as follows: (1) We give the vertex face total chromatic number for all outerplanar graphs and modulus 3-regular maximal planar graphs. (2) We prove that if G is a maximal planar graph or a lower degree planar graph, i.e., ∠(G) ≤ 3, then χ13(G) ≤ 6. © 1996 John Wiley & Sons, Inc. 相似文献
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WANGWEIFAN ZHANGKEMIN 《高校应用数学学报(英文版)》1997,12(4):455-462
A Planar graph g is called a ipseudo outerplanar graph if there is a subset v.∈V(G),[V.]=i,such that G-V. is an outerplanar graph in particular when G-V.is a forest ,g is called a i-pseudo-tree .in this paper.the following results are proved;(1)the conjecture on the total coloring is true for all 1-pseudo-outerplanar graphs;(2)X1(G) 1 fo any 1-pseudo outerplanar graph g with △(G)≥3,where x4(G)is the total chromatic number of a graph g. 相似文献
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A graph is called H-free if it contains no copy of H. Denote by f
n
(H) the number of (labeled) H-free graphs on n vertices. Erdős conjectured that f
n
(H) ≤ 2(1+o(1))ex(n,H). This was first shown to be true for cliques; then, Erdős, Frankl, and R?dl proved it for all graphs H with χ(H)≥3. For most bipartite H, the question is still wide open, and even the correct order of magnitude of log2
f
n
(H) is not known. We prove that f
n
(K
m,m
) ≤ 2
O
(n
2−1/m
) for every m, extending the result of Kleitman and Winston and answering a question of Erdős. This bound is asymptotically sharp for m∈{2,3}, and possibly for all other values of m, for which the order of ex(n,K
m,m
) is conjectured to be Θ(n
2−1/m
). Our method also yields a bound on the number of K
m,m
-free graphs with fixed order and size, extending the result of Füredi. Using this bound, we prove a relaxed version of a
conjecture due to Haxell, Kohayakawa, and Łuczak and show that almost all K
3,3-free graphs of order n have more than 1/20·ex(n,K
3,3) edges. 相似文献
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《Discrete Mathematics》2023,346(1):113162
The graph coloring game is a two-player game in which the two players properly color an uncolored vertex of G alternately. The first player wins the game if all vertices of G are colored, and the second wins otherwise. The game chromatic number of a graph G is the minimum integer k such that the first player has a winning strategy for the graph coloring game on G with k colors. There is a lot of literature on the game chromatic number of graph products, e.g., the Cartesian product and the lexicographic product. In this paper, we investigate the game chromatic number of the strong product of graphs, which is one of major graph products. In particular, we completely determine the game chromatic number of the strong product of a double star and a complete graph. Moreover, we estimate the game chromatic number of some King's graphs, which are the strong products of two paths. 相似文献
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Bojan Vučković 《Discrete Mathematics》2018,341(5):1472-1478
An adjacent vertex distinguishing total -coloring of a graph is a proper total -coloring of such that any pair of adjacent vertices have different sets of colors. The minimum number needed for such a total coloring of is denoted by . In this paper we prove that if , and in general. This improves a result in Huang et al. (2012) which states that for any graph with . 相似文献
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The equitable total chromatic number Χet (G) of a graphG is the smallest integerk for whichG has a total k-coloring such that the number of vertices and edges in any two color classes differ by at most one. In this paper, we determine the equitable total chromatic number of one class of the graphs. 相似文献