题目：(3, 1)∗ -choosability of planar graphs

报告人：Min Chen 浙江师范大学

时间：6月22日 11:00-12:00

地点：1518

摘要: An (L, d) ∗ -coloring is a mapping π that assigns a color π(v) ∈ L(v) to each vertex v ∈ V (G) so that at most d neighbors of v receive color π(v). A graph G is said to be (k, d) ∗ -choosable if it admits an (L, d) ∗ -coloring for every list assignment L with |L(v)| ≥ k for all v ∈ V (G). In this talk, firstly, I will show some known results on improper list coloring of (planar) graphs with some restrictions. Then, I will give a short proof of our recent result which says that every planar graph without adjacent triangles and 6-cycles is (3, 1)∗ -choosable. This partially answers the question proposed by Xu and Zhang that every planar graphs without adjacent triangles is (3, 1)∗ - choosable. This is joint work with Andr′e Raspaud and Weifan Wang. Keyword: Planar graphs; Improper choosability; Cycle