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arXiv · 0904.1319

Circular Coloring and Mycielski Construction

Meysam Alishahi·Hossein Hajiabolhassan
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Abstract

In this paper, we investigate circular chromatic number of Mycielski construction of graphs. It was shown in \cite{MR2279672} that $t^{\rm th}$ Mycielskian of the Kneser graph $KG(m,n)$ has the same circular chromatic number and chromatic number provided that $m+t$ is an even integer. We prove that if $m$ is large enough, then $χ(M^t(KG(m,n)))=χ_c(M^t(KG(m,n)))$ where $M^t$ is $t^{\rm th}$ Mycielskian. Also, we consider the generalized Kneser graph $KG(m,n,s)$ and show that there exists a threshold $m(n,s,t)$ such that $χ(M^t(KG(m,n,s)))=χ_c(M^t(KG(m,n,s)))$ for $m\geq m(n,s,t)$.

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Meysam Alishahi, Hossein Hajiabolhassan. 2009-04-08. Circular Coloring and Mycielski Construction. https://arxiv.org/abs/0904.1319

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