The Reduced Genus of a Multigraph

Patrice Ossona de Mendez (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

We define here the reduced genus of a multigraph as the minimum genus of a hypergraph having the same adjacencies with the same multiplicities. Through a study of embedded hypergraphs, we obtain new bounds on the coloring number, clique number and point arboricity of simple graphs of a given reduced genus. We present some new related problems on graph coloring and graph representation.

Domaines: Combinatoire [math.CO]

Patrice Ossona de Mendez. The Reduced Genus of a Multigraph. STACS 99, 1999, Triest, Germany. pp.16-31. ⟨hal-00005638⟩