Subcubic triangle-free graphs have fractional chromatic number at most $14/5$

Zdeněk Dvořák (1) , Jean-Sébastien Sereni (2) , Jan Volec (3)

1 IUUK - Computer Science Institute of Charles University [Prague]
2 ORPAILLEUR - Knowledge representation, reasonning
3 DIMAP - Centre for Discrete Mathematics and its Applications [Warwick]

We prove that every subcubic triangle-free graph has fractional chromatic number at most 14/5, thus confirming a conjecture of Heckman and Thomas [A new proof of the independence ratio of triangle-free cubic graphs. Discrete Math. 233 (2001), 233--237].

Mots clés: Fractional coloring; independent sets; weighted independent sets

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Zdeněk Dvořák, Jean-Sébastien Sereni, Jan Volec. Subcubic triangle-free graphs have fractional chromatic number at most $14/5$. Journal of the London Mathematical Society, 2014, 89 (3), pp.641--662. ⟨10.1112/jlms/jdt085⟩. ⟨hal-00779634v3⟩