A Characterization of Graphs with Fractional Total
نویسندگان
چکیده
For a simple graph of maximum degree ∆, the complexity of computing the fractional total chromatic number is unknown. Kilakos and Reed proved it lies between ∆+1 and ∆+2, and so we can approximate it within 1. In this paper, we strengthen this by characterizing exactly those simple graphs with fractional total chromatic number ∆ + 2. This yields a simple linear-time algorithm to determine whether a given graph has fractional chromatic number ∆ + 2.
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