The last fraction of a fractional conjecture

František Kardoš (1, 2) , Daniel Král' (1) , Jean-Sébastien Sereni (3, 4)

1 ITI - Institut teoretické informatiky
2 Institute of Mathematics
3 KAM - Department of Applied Mathematics (KAM)
4 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

Reed conjectured that for every ε>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+ε. 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.

Mots clés: fractional coloring; total coloring; girth

Domaines: Mathématique discrète [cs.DM]

František Kardoš, Daniel Král', Jean-Sébastien Sereni. The last fraction of a fractional conjecture. SIAM Journal on Discrete Mathematics, 2010, 24 (2), pp.699--707. ⟨10.1137/090779097⟩. ⟨hal-00495646⟩