# The Extremal Function For Noncomplete Minors

@article{Myers2005TheEF,
title={The Extremal Function For Noncomplete Minors},
author={Joseph Samuel Myers and Andrew Thomason},
journal={Combinatorica},
year={2005},
volume={25},
pages={725-753}
}
• Published 1 December 2005
• Mathematics
• Combinatorica
We investigate the maximum number of edges that a graph G can have if it does not contain a given graph H as a minor (subcontraction). Let $$c{\left( H \right)} = \inf {\left\{ {c:e{\left( G \right)} \geqslant c{\left| G \right|}{\text{implies}}{\kern 1pt} {\kern 1pt} G \succ H} \right\}}.$$We define a parameter γ(H) of the graph H and show that, if H has t vertices, then $$c{\left( H \right)} = {\left( {\alpha \gamma {\left( H \right)} + o{\left( 1 \right)}} \right)}t{\sqrt {\log {\kern 1pt… On the extremal function for graph minors • Mathematics, Computer Science Journal of Graph Theory • 2022 It is shown that if H has average degree d, then c(H)le (0.319\ldots+o_d(1)|H|\sqrt{\log d}$$ is an explicitly defined constant, which matches a corresponding lower bound shown to hold for almost all such graphs by Norin, Reed, Wood and the first author.
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