# The Extremal Function for Complete Minors

@article{Thomason2001TheEF,
title={The Extremal Function for Complete Minors},
author={Andrew Thomason},
journal={J. Comb. Theory, Ser. B},
year={2001},
volume={81},
pages={318-338}
}
• A. Thomason
• Published 1 March 2001
• Mathematics
• J. Comb. Theory, Ser. B
Let c(t) be the minimum number c such that every graph G with e(G)?c|G| contracts to a complete graph Kt. We show thatc(t)=(?+o(1))tlogtwhere ?=0.319... is an explicit constant. Random graphs are extremal graphs.
268 Citations
Extremal Functions for Graph Minors
The extremal problem for graph minors is to determine, given a fixed graph H, how many edges a graph G can have if it does not have H as a minor. It turns out that the extremal graphs are
Logarithmically small minors and topological minors
• R. Montgomery
• Mathematics, Computer Science
J. Lond. Math. Soc.
• 2015
This paper proves the conjecture of Fiorini, Joret, Theis and Wood that any graph with n vertices and average degree at least c(t)+ε must contain a Kt ‐minor consisting of at most C(ε,t)logn vertices.
Minor Extremal Problems Using Turan Graphs
• Mathematics
• 2007
The extremal number ex(n;MKp) denotes the maximum number of edges of a graph of order n not containing a complete graph Kp as a minor. In this paper we find a lower bound for this extremal number
Graphs without minor complete subgraphs
• Mathematics
Discret. Math.
• 2007
The edge-density for K2, t minors
• Mathematics
J. Comb. Theory, Ser. B
• 2011
The extremal function for Petersen minors
• Mathematics
J. Comb. Theory, Ser. B
• 2018
The extremal function for structured sparse minors
Let c(H) be the smallest value for which e(G)/|G| > c(H) implies H is a minor of G. We show a new upper bound on c(H), which improves previous bounds for graphs with a vertex partition where some
Ju l 2 01 9 ON THE EXTREMAL FUNCTION FOR GRAPH MINORS
For a graph H , let c(H) = inf{c : e(G) > c|G| implies G ≻ H }, where G ≻ H means that H is a minor of G. We show that if H has average degree d, then c(H) ≤ (0.319 . . .+ od(1))|H | √ log d where