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- W2755482418 abstract "A graph is $k$-degenerate if every subgraph has minimum degree at most $k$. We provide lower bounds on the size of a maximum induced 2-degenerate subgraph in a triangle-free planar graph. We denote the size of a maximum induced 2-degenerate subgraph of a graph $G$ by $alpha_2(G)$. We prove that if $G$ is a connected triangle-free planar graph with $n$ vertices and $m$ edges, then $alpha_2(G) geq frac{6n - m - 1}{5}$. By Euler's Formula, this implies $alpha_2(G) geq frac{4}{5}n$. We also prove that if $G$ is a triangle-free planar graph on $n$ vertices with at most $n_3$ vertices of degree at most three, then $alpha_2(G) geq frac{7}{8}n - 18 n_3$." @default.
- W2755482418 created "2017-09-25" @default.
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- W2755482418 date "2017-09-12" @default.
- W2755482418 modified "2023-10-10" @default.
- W2755482418 title "Induced 2-degenerate Subgraphs of Triangle-free Planar Graphs" @default.
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