The last fraction of a fractional conjecture

Abstract

Reed conjectured that for every $\epsilon >0$ 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 $\Delta +1+\epsilon$. 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.

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

References in corpus (1)

• Fractional total colourings of graphs of high girth