On the fractional f-chromatic index of a graph

Abstract

For a graph G, we assign a positive integer f(v) to each vertex v∈V(G). The f-chromatic index of G, denoted by , is the minimum number of f-matchings needed to partition E(G), where an f-matching of G is the edge set of a (0, f)-factor of G. In this paper, we give the exact value of the fractional f-chromatic index of a graph.

Keywords:

• graph
• fractional edge-colouring
• f-colouring
• f-chromatic index
• (0, f)-factor

2000 AMS Subject Classifications :

• 05C15
• 05C70

Acknowledgements

We would like to thank the referee for reading our manuscript carefully and for his(her) helpful comments. This work is supported by NSFC (10901097), NSFC (10871119), RFDP (200804220001), Tianyuan Youth Foundation of Mathematics (10926099) of China, NSF of Shandong (ZR2010AQ003), Promotional Foundation (2005BS01016) for Middle-aged or Young Scientists of Shandong Province, SRI of SPED (J07WH05), DRF and UF (XJ0609) of QFNU.