A Note on 3-choosability of Planar Graphs Related to Montanssier's Conjecture

摘要

For a given list assignment L = {L(v) : v is an element of V (G)}, a graph G = (V, E) is L-colorable if there exists a proper coloring c of G such that c(v) E L(v) for all v E V. If G is L-colorable for every list assignment L having vertical bar L(v)vertical bar >= k for all v is an element of V, then G is said to be k-choosable. Montassier (Inform. Process. Lett. 99 (2006) 68-71) conjectured that every planar graph without cycles of length 4, 5, 6, is 3-choosable. In this paper, we prove that every planar graph without 5-, 6- and 10-cycles, and without two triangles at distance less than 3 is 3-choosable.