Fractional total colourings of graphs of high girth

2009/11/14 by Kaiser, Tomas, King, Andrew, Kral, Daniel
#05C15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0911.2808

Abstract

Reed conjectured that for every epsilon>0 and Delta there exists g such that the fractional total chromatic number of a graph with maximum degree Delta and girth at least g is at most Delta+1+epsilon. We prove the conjecture for Delta=3 and for even Delta>=4 in the following stronger form: For each of these values of Delta, there exists g such that the fractional total chromatic number of any graph with maximum degree Delta and girth at least g is equal to Delta+1.

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