Maximum 4-Degenerate Subgraph of a Planar Graph

[摘要] A graph $G$ is $k$-degenerate if it can be transformed into an empty graph by subsequent removals of vertices of degree $k$ or less. We prove that every connected planar graph with average degree $d \ge  2$ has a $4$-degenerate induced subgraph containing

[学科分类] 离散数学和组合数学

[关键词] Degenerate subgraphs;Planar graphs;List colouring