Every triangle-free induced subgraph of the triangular lattice is $(5m,2m)$-choosable

Yves Aubry (1, 2) , Jean-Christophe Godin (2) , Olivier Togni (3)

1 IML - Institut de mathématiques de Luminy
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

A graph $G$ is $(a,b)$-choosable if for any color list of size $a$ associated with each vertex, one can choose a subset of $b$ colors such that adjacent vertices are colored with disjoint color sets. This paper proves that for any integer $m\ge 1$, every finite triangle-free induced subgraph of the triangular lattice is $(5m,2m)$-choosable.

Mots clés: weighted graph; Radio channel assignment; triangular lattice; choosability; weighted graph.

Domaines: Combinatoire [math.CO]

Yves Aubry, Jean-Christophe Godin, Olivier Togni. Every triangle-free induced subgraph of the triangular lattice is $(5m,2m)$-choosable. Discrete Applied Mathematics, 2014, 166, pp.51--58. ⟨10.1016/j.dam.2013.09.028⟩. ⟨hal-00631398⟩