Induced 2-Degenerate Subgraphs of Triangle-Free Planar Graphs
نویسندگان
چکیده
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 α2(G). We prove that if G is a connected triangle-free planar graph with n vertices and m edges, then α2(G) ≥ 6n−m−1 5 . By Euler’s Formula, this implies α2(G) ≥ 4 5 n. We also prove that if G is a triangle-free planar graph on n vertices with at most n3 vertices of degree at most three, then α2(G) ≥ 7 8 n− 18n3.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 25 شماره
صفحات -
تاریخ انتشار 2018