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On the complexity of the circular chromatic number

Hatami, H ; Sharif University of Technology | 2004

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  1. Type of Document: Article
  2. DOI: 10.1002/jgt.20022
  3. Publisher: Wiley-Liss Inc , 2004
  4. Abstract:
  5. Circular chromatic number, χc 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)= χc(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 ≥ 2 and n ≥ 3, for a given graph G with χ(G)= n, it is NP-complete to verify if χc(G)≤ n -1/k. © 2004 Wiley Periodicals, Inc
  6. Keywords:
  7. Chromatic number ; Circular chromatic number ; Np-hard
  8. Source: Journal of Graph Theory ; Volume 47, Issue 3 , 2004 , Pages 226-230 ; 03649024 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.20022