3-degenerate induced subgraph of a planar graph

Abstract

A graph $G$ is $d$-degenerate if every non-null subgraph of $G$ has a vertex of degree at most $d$. We prove that every $n$-vertex planar graph has a $3$-degenerate induced subgraph of order at least $3n/4$.

28 pages, 12 figures

References in corpus (3)

• Minimum Size of Feedback Vertex Sets of Planar Graphs of Girth at least Five
• Planar graphs have two-coloring number at most 8
• Maximum 4-degenerate subgraph of a planar graph