منابع مشابه
Clique and chromatic number of circular-perfect graphs
A main result of combinatorial optimization is that clique and chromatic number of a perfect graph are computable in polynomial time (Grötschel, Lovász and Schrijver 1981). Circular-perfect graphs form a well-studied superclass of perfect graphs. We extend the above result for perfect graphs by showing that clique and chromatic number of a circularperfect graph are computable in polynomial time...
متن کاملchromatic and clique numbers of a class of perfect graphs
let $p$ be a prime number and $n$ be a positive integer. the graph $g_p(n)$ is a graph with vertex set $[n]={1,2,ldots ,n}$, in which there is an arc from $u$ to $v$ if and only if $uneq v$ and $pnmid u+v$. in this paper it is shown that $g_p(n)$ is a perfect graph. in addition, an explicit formula for the chromatic number of such graph is given.
متن کاملFractional chromatic number and circular chromatic number for distance graphs with large clique size
Let Z be the set of all integers and M a set of positive integers. The distance graph G(Z,M) generated by M is the graph with vertex set Z and in which i and j are adjacent whenever |i − j| ∈ M . Supported in part by the National Science Foundation under grant DMS 9805945. Supported in part by the National Science Council, R. O. C., under grant NSC892115-M-110-012.
متن کاملColouring perfect graphs with bounded clique number
A graph is perfect if the chromatic number of every induced subgraph equals the size of its largest clique, and an algorithm of Grötschel, Lovász, and Schrijver [9] from 1988 finds an optimal colouring of a perfect graph in polynomial time. But this algorithm uses the ellipsoid method, and it is a well-known open question to construct a “combinatorial” polynomial-time algorithm that yields an o...
متن کاملThe Clique-rank of 3-chromatic Perfect Graphs
The clique-rank of a perfect graph G introduced by Fonlupt and Sebö is the linear rank of the incidence matrix of the maximum cliques of G. We study this rank for 3-chromatic perfect graphs. We prove that if, in addition, G is diamond-free, G has two distinct colorations. An immediate consequence is that the Strong Perfect Graph Conjecture holds for diamond-free graphs and for graphs with cliqu...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2016
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2015.09.008