A linear-time algorithm for finding a complete graph minor in a dense graph

Details A linear-time algorithm for finding a complete graph minor in a dense graph A linear-time algorithm for finding a complete graph minor in a dense graph

2012-02-13

arxiv.org/abs/1202.2624v1

Mathematics

Combinatorics

6 pages, 0 figures

Scientific paper

Let g(t) be the minimum number such that every graph G with average degree d(G) \geq g(t) contains a K_{t}-minor. Such a function is known to exist, as originally shown by Mader. Kostochka and Thomason independently proved that g(t) \in \Theta(t*sqrt{log t}). This article shows that for all fixed \epsilon > 0 and fixed sufficiently large t \geq t(\epsilon), if d(G) \geq (2+\epsilon)g(t) then we can find this K_{t}-minor in linear time. This improves a previous result by Reed and Wood who gave a linear-time algorithm when d(G) \geq 2^{t-2}.

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