Planar graphs without adjacent cycles of length at most seven are 3-colorable

O.V. Borodin (1) , Mickael Montassier (2) , André Raspaud (2)

1 NSU - Institute of Mathematics, NSU - Russia
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We prove that every planar graph in which no $i$-cycle is adjacent to a $j$-cycle whenever $3\leq i\leq j\leq 7$ is 3-colorable and pose some related problems on the 3-colorability of planar graphs.

Domaines: Mathématique discrète [cs.DM]

O.V. Borodin, Mickael Montassier, André Raspaud. Planar graphs without adjacent cycles of length at most seven are 3-colorable. Discrete Mathematics, 2010, 310 (1), pp.167-173. ⟨hal-00401710⟩