The Last Fraction of a Fractional Conjecture
Copyright policy )The Last Fraction of a Fractional Conjecture
Reed conjectured that for every $\varepsilon>0$ and every integer $Δ$, there exists $g$ such that the fractional total chromatic number of every graph with maximum degree $Δ$ and girth at least $g$ is at most $Δ+1+\varepsilon$. The conjecture was proven to be true when $Δ=3$ or $Δ$ is even. We settle the conjecture by proving it for the remaining cases.
A typo has been corrected in the introduction (concerning the citation of the result by Ito, Kennedy and Reed)
- Université Paris Cité France
- French National Centre for Scientific Research France
- Institute of Mathematics Belarus
- Czech Academy of Sciences Czech Republic
- Charles University Czech Republic
girth, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], total coloring, 05C15, fractional coloring, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
girth, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], total coloring, 05C15, fractional coloring, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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