Fractional total colourings of graphs of high girth |
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| Authors: | Tomá &scaron Kaiser,Andrew King,Daniel Krá l? |
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| Affiliation: | aDepartment of Mathematics and Institute for Theoretical Computer Science, University of West Bohemia, Univerzitní 8, 306 14 Plzeň, Czech Republic;bInstitute for Theoretical Computer Science, Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00 Prague, Czech Republic |
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| Abstract: | Reed conjectured that for every ?>0 and Δ there exists g such that the fractional total chromatic number of a graph with maximum degree Δ and girth at least g is at most Δ+1+?. We prove the conjecture for Δ=3 and for even Δ?4 in the following stronger form: For each of these values of Δ, there exists g such that the fractional total chromatic number of any graph with maximum degree Δ and girth at least g is equal to Δ+1. |
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| Keywords: | Total colouring Fractional total chromatic number |
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