Representations by Contact and Intersection of Segments

Hubert de Fraysseix (1) , Patrice Ossona de Mendez (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

A necessary and sufficient condition is given for a connected bipartite graph to be the incidence graph of a contact family of segments and points. We deduce that any four-connected three-colorable plane graph is the contact graph of a family of segments and that any four-colored planar graph without an induced C4 using four colors is the intersection graph of a family of straight line segments.

Domaines: Combinatoire [math.CO]

Hubert de Fraysseix, Patrice Ossona de Mendez. Representations by Contact and Intersection of Segments. Algorithmica, 2007, 47 (4), pp.453-463. ⟨10.1007/s00453-006-0157-x⟩. ⟨hal-00138575⟩