Computing the clique number and chromatic number of a general graph are well-known NP-Hard problems. Codenotti etal., (1998) showed that computing clique number and chromatic number are both NP-Hard problems for the class of circulant graphs. We show that computing clique number is NP-Hard ...
The list chromatic number of a graph was introduced by Erdös et al. [2] and independently by Vizing [9] as a natural extension of the chromatic number. However, the behavior of the list chromatic number is much more subtle than that of the chromatic number and it is more difficult to...
GraphTheory CliqueNumber compute clique number of graph MaximumClique find maximum clique in graph Calling Sequence Parameters Options Description Examples References Compatibility Calling Sequence CliqueNumber( G ) CliqueNumber( G , opt ) MaximumClique(
ω, ∆ and χ. J. Graph Theory 27 (1998) 177–212. 14]]>Claw-free graphsChromatic numberList coloringChudnovsky and Seymour proved that every connected claw-free graph that contains a stable set of size 3 has chromatic number at most twice its clique number. We improve this for small ...
4) clique partition number 团划分数 1. This paper discusses clique covering number and clique partition number on the line graph and total graph of n Sun graph. 主要讨论n-太阳图的线图及全图的团覆盖数和团划分数,得出了n-太阳图的线图及全图的覆团盖数与团划分数相等且都是n的倍数。 2. ...
Summary: The clique-chromatic number of a graph $G = (V,E)$ denoted by $χ_{c }(G)$ is the smallest integer $k$ such that there exists a partition of the vertex set of $G$ into $k$ subsets with the property that no maximal clique of $G$ is contained in any of the subsets...
G - graph size - (optional) integer or range; size of clique to find Description • FindCliquereturns a list of vertices which comprise acliquein the graphG. The optional parametersizespecifies a size for the clique. Ifsizeis omitted,FindCliquebehaves identically toMaximumCliqueand returns a...
The strong chromatic index of G is equal to the chromatic number of the square of the line graph of G. The chromatic number of the square of the line graph of G is greater than or equal to the clique number of the square of the line graph of G, denoted by ω(L). In this note...
On the query complexity of clique size and maximum satisfiability - Chang - 1996 () Citation Context ...uery complexity (that is, the number of queries to an NP oracle needed to solve a given problem) has been shown to be a very useful tool for understanding the complexity of ...
We study the problem of approximating the number of k k k -cliques in a graph when given query access to the graph. We consider the standard query model fo... T Eden,D Ron,C Seshadhri 被引量: 6发表: 2017年 The circular chromatic number of the Mycielskian of G(k)(d) In a se...