The last fraction of a fractional conjecture

Details The last fraction of a fractional conjecture The last fraction of a fractional conjecture

2009-12-03

arxiv.org/abs/0912.0683v2

Mathematics

Combinatorics

A typo has been corrected in the introduction (concerning the citation of the result by Ito, Kennedy and Reed)

Scientific paper

Reed conjectured that for every $\varepsilon>0$ and every integer $\Delta$, there exists $g$ such that the fractional total chromatic number of every graph with maximum degree $\Delta$ and girth at least $g$ is at most $\Delta+1+\varepsilon$. The conjecture was proven to be true when $\Delta=3$ or $\Delta$ is even. We settle the conjecture by proving it for the remaining cases.

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