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On the Complexity of the Circular Chromatic Number

Hamed Hatami·Ruzbeh Tusserkani
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Abstract

Circular chromatic number, $χ_c$ is a natural generalization of chromatic number. It is known that it is \NP-hard to determine whether or not an arbitrary graph $G$ satisfies $χ(G) = χ_c(G)$. In this paper we prove that this problem is \NP-hard even if the chromatic number of the graph is known. This answers a question of Xuding Zhu. Also we prove that for all positive integers $k \ge 2$ and $n \ge 3$, for a given graph $G$ with $χ(G)=n$, it is \NP-complete to verify if $χ_c(G) \le n- \frac{1}{k}$.

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BibTeXRIS

Hamed Hatami, Ruzbeh Tusserkani. 2006-12-31. On the Complexity of the Circular Chromatic Number. https://arxiv.org/abs/cs/0701007

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