Get access

On the Circular Chromatic Number of Graph Powers

Authors

  • Hossein Hajiabolhassan,

    1. DEPARTMENT OF MATHEMATICAL SCIENCES, SHAHID BEHESHTI UNIVERSITY, G.C., TEHRAN, IRAN
    Search for more papers by this author
    • The research of this author was partially supported by Shahid Beheshti University.

  • Ali Taherkhani

    1. DEPARTMENT OF MATHEMATICS, INSTITUTE FOR ADVANCED STUDIES IN BASIC SCIENCES (IASBS), IRAN
    Search for more papers by this author
    • Ali Taherkhani gratefully acknowledges support by the Institute for Advanced Studies in Basic Sciences (IASBS) Research Council under grant no. G2011IASBS148.


Abstract

This article intends to study some functors math formula from the category of graphs to itself such that, for any graph G, the circular chromatic number of math formula is determined by that of G. In this regard, we investigate some coloring properties of graph powers. We show that math formula provided that math formula. As a consequence, we show that if math formula, then math formula. In particular, math formula and math formula has no subgraph with circular chromatic number equal to math formula. This provides a negative answer to a question asked in (X. Zhu, Discrete Math, 229(1–3) (2001), 371–410). Moreover, we investigate the nth multichromatic number of subdivision graphs. Also, we present an upper bound for the fractional chromatic number of subdivision graphs. Precisely, we show that math formula.

Ancillary