Edge-Maximal Graphs on Surfaces

Author:

McDiarmid Colin,Wood David R.

Abstract

AbstractWe prove that for every surface ∑ of Euler genus g, every edge-maximal embedding of a graph in ∑ is at most O(g) edges short of a triangulation of ∑. This provides the first answer to an open problem of Kainen (1974).

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Robust Connectivity of Graphs on Surfaces;SIAM Journal on Discrete Mathematics;2022-06

2. Edge‐maximal graphs on orientable and some nonorientable surfaces;Journal of Graph Theory;2021-07-06

3. Locally Hamiltonian Graphs and Minimal Size of Maximal Graphs on a Surface;The Electronic Journal of Combinatorics;2020-05-29

4. On the purity of minor-closed classes of graphs;Journal of Combinatorial Theory, Series B;2019-03

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