Edge-Face Coloring of Plane Graphs with Maximum Degree Nine

Jean-Sébastien Sereni (1, 2) , Matej Stehlík (3)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 KAM - Department of Applied Mathematics (KAM)
3 G-SCOP_OC - Optimisation Combinatoire

An edge-face coloring of a plane graph with edge set E and face set F is a coloring of the elements of E ∪ F so that adjacent or incident elements receive different colors. Borodin [Discrete Math 128(1-3):21-33, 1994] proved that every plane graph of maximum degree ∆≥10 can be edge-face colored with ∆+1 colors. We extend Borodin's result to the case where ∆=9.

Mots clés: graph coloring; plane graph; edge-face coloring

Domaines: Mathématique discrète [cs.DM]

Jean-Sébastien Sereni, Matej Stehlík. Edge-Face Coloring of Plane Graphs with Maximum Degree Nine. Journal of Graph Theory, 2011, 66 (4), pp.332-346. ⟨10.1002/jgt.20506⟩. ⟨hal-00574164⟩