On Coloring Properties of Graph Powers

Abstract

This paper studies some coloring properties of graph powers. We show that3n+1 has no subgraph with circular chromatic number equal to 6n+12n+1 . This provides a negative answer to a question asked in [Xuding Zhu, Circular chromatic number: a survey, Discrete Math., 229(1-3): 2001]. Also, we present an upper bound for the fractional chromatic number of subdivision graphs. Precisely, we show that. Finally, we investigate the nth multichromatic number of subdivision graphs.