Fuzzy chromatic numberPerfect fuzzy graphPerfect fuzzy graph theoremPerfect graphs have a significant role in graph theory in terms of structure as well as application. This article embarked a comprehensive study on perfect fuzzy graphs attempted to obtain the fuzzy analog of the famous weak and ...
Brooks' theorem: For any connected undirected graph G with maximum degree Δ, the chromatic number of G is at most Δ unless G is a complete graph or an odd cycle, in which case the chromatic number is Δ + 1.对于任何具有最大度数Δ的连通无向图G,除非G是一个完全图或一个奇圈,否则G的...
chromatic number (mathematics) The smallest number of colours necessary to colour the nodes of agraphso that no two adjacent nodes have the same colour. See also:four colour map theorem. Graph Theory Lessons. Eric Weisstein's World Of Mathematics. ...
Given a graph H and an integer k≥1, the Gallai–Ramsey number GRk(H) is defined to be the minimum integer n such that every k-edge coloring of the complete graph Kn contains either a rainbow (all different colored) triangle or a monochromatic copy of H. In this paper, we study Gall...
Consequently, we prove that the chromatic number of G is at most T(G)+1 with equality if and only if G is an odd cycle or a complete graph, which implies Brook's theorem. A generalization of this result is also given. 展开
摘要: We prove that the chromatic number of an oriented matroid O of rank r 3 is at most r + 1 with equality if and only if O is the oriented matroid of an orientation of K r + 1, the complete graph on r + 1 vertices.
The graph G is A -colorable if for any function f ∈ F ( G , A ), there is a function c : V ( G ) A such that for every directed e = u v ∈ E ( G ), c ( u ) c ( v )≠ f ( e ). The group chromatic number χ 1 ( G ) of a graph G is the minimum m ...
3. It is discussed that the vertex chromatic numbers on complement double graph of complete graph,cycle and path in this paper. 文章研究了完全图、圈、路的补倍图的点色数。更多例句>> 2) point color number 点色数 1. The 3 color theorem and 4 color theorem of maximum plate graph are ...
Theorem 1.1 [3] Let G be a non-complete connected graph with n vertices, chromatic number χ and distance Laplacian spectral radius ∂1L. Then∂1L≥n+⌈nχ⌉. Motivated by Theorem 1.1, we raise the following natural questions. Problem 1 Is the spectral radius ∂1L the only distanc...
In order to complete the proof of the theorem, let us show that if G is a block graph with αmin(G)=α(G), largest clique size ω(G) and outside from the basic class, then it can be obtained from a block graph H with αmin(H)=α(H) and the largest clique size ω(H)≤ω...