منابع مشابه
Generalised Mycielski Graphs and Bounds on Chromatic Numbers
We prove that the coindex of the box complex B(H) of a graph H can be measured by the generalised Mycielski graphs which admit a homomorphism to it. As a consequence, we exhibit for every graph H a system of linear equations solvable in polynomial time, with the following properties: If the system has no solutions, then coind(B(H))+2 ≤ 3; if the system has solutions, then χ(H) ≥ 4. We generalis...
متن کاملCircular chromatic number for iterated Mycielski graphs
For a graph G, let M(G) denote the Mycielski graph of G. The t-th iterated Mycielski graph of G, M(G), is defined recursively by M0(G) = G and M(G)= M(Mt−1(G)) for t ≥ 1. Let χc(G) denote the circular chromatic number of G. We prove two main results: 1) Assume G has a universal vertex x, then χc(M(G)) = χ(M(G)) if χc(G − x) > χ(G − x) − 1/2 and G is not a star, otherwise χc(M(G)) = χ(M(G)) − 1/...
متن کاملCircular Chromatic Number and Mycielski Graphs
As a natural generalization of graph coloring, Vince introduced the star chromatic number of a graph G and denoted it by χ∗(G). Later, Zhu called it circular chromatic number and denoted it by χc(G). Let χ(G) be the chromatic number of G. In this paper, it is shown that if the complement of G is non-hamiltonian, then χc(G)=χ(G). Denote by M(G) the Mycielski graph of G. Recursively define Mm(G)=...
متن کاملGeneralized edge-chromatic numbers and additive hereditary properties of graphs
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let P and Q be hereditary properties of graphs. The generalized edge-chromatic number ρQ(P) is defined as the least integer n such that P ⊆ nQ. We investigate the generalized edge-chromatic numbers of the properties → H, Ik, Ok, W∗ k , Sk and Dk.
متن کاملA lower bound on the chromatic number of Mycielski graphs
In this work we give a new lower bound on the chromatic number of a Mycielski graph Mi. The result exploits a mapping between the coloring problem and a multiprocessor task scheduling problem. The tightness of the bound is proved for i = 1; : : : ; 8. c © 2001 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.12.011