Odd cycle transversals and independent sets in fullerene graphs

Luerbio Faria (1) , Sulamita Klein (2) , Matej Stehlik (3)

1 UERJ - Universidade do Estado do Rio de Janeiro [Brasil] = Rio de Janeiro State University [Brazil] = Université d'État de Rio de Janeiro [Brésil]
2 DCC - Departamento de Ciência Da Computação [Rio de Janeiro]
3 G-SCOP_OC - Optimisation Combinatoire

A fullerene graph is a cubic bridgeless plane graph with all faces of size 5 and 6. We show that every fullerene graph on n vertices can be made bipartite by deleting at most sqrt{12n/5} edges, and has an independent set with at least n/2-sqrt{3n/5} vertices. Both bounds are sharp, and we characterise the extremal graphs. This proves conjectures of Doslic and Vukicevic, and of Daugherty. We deduce two further conjectures on the independence number of fullerene graphs, as well as a new upper bound on the smallest eigenvalue of a fullerene graph.

Mots clés: fullerene graph; odd cycle transversal; independent set; max-cut

Domaines: Mathématique discrète [cs.DM]

Luerbio Faria, Sulamita Klein, Matej Stehlik. Odd cycle transversals and independent sets in fullerene graphs. SIAM Journal on Discrete Mathematics, 2012, 26 (3), pp.1458-1469. ⟨10.1137/120870463⟩. ⟨hal-00787837⟩