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Selected Works

2008

Extremal function

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On KS,T-Minors In Graphs With Given Average Degree, A. V. Kostochka, N. Prince Dec 2007

On KS,T-Minors In Graphs With Given Average Degree, A. V. Kostochka, N. Prince

Noah Prince

Let D(H) be the minimum d such that every graph G with average degree d has an H-minor. Myers and Thomason found good bounds on D(H) for almost all graphs H and proved that for 'balanced' H random graphs provide extremal examples and determine the extremal function. Examples of 'unbalanced graphs' are complete bipartite graphs Ks,t for a fixed s and large t. Myers proved upper bounds on D(Ks,t ) and made a conjecture on the order of magnitude of D(Ks,t ) for a fixed s and …