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

摘要

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 ≥ 1, every finite triangle-free induced subgraph of the triangular lattice is (5m, 2m)-choosable.