Generalised Mycielski graphs, signature systems, and bounds on chromatic numbers
نویسندگان
چکیده
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...
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We give upper bounds for the generalised acyclic chromatic number and generalised acyclic edge chromatic number of graphs with maximum degree d, as a function of d. We also produce examples of graphs where these bounds are of the correct order.
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)=...
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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 کاملGeneralised Mycielski Graphs as Topological Cliques
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.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2017
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2016.09.007