TY - JOUR

T1 - On K s,t-minors in graphs with given average degree, II

AU - Kostochka, A. V.

AU - Prince, N.

N1 - Funding Information:
The research of the first author is supported in part by NSF grant DMS-0965587 , by the Ministry of Education and Science of the Russian Federation (Contract no. 14.740.11.0868) and by grant 09-01-00244 of the Russian Foundation for Basic Research .

PY - 2012/12/28

Y1 - 2012/12/28

N2 - Let Ks,t* denote the graph obtained from Ks, t by adding all edges between the s vertices of degree t in it. We show how to adapt the argument of our previous paper [A.V. Kostochka, N. Prince, On Ks, t-minors in graphs with given average degree, Discrete Math. 308 (2008) 4435-4445] to prove that if tlog 2t<1000s, then every graph G with average degree at least t+8slog 2s has a Ks,t* minor. This refines a corresponding result by Kühn and Osthus.

AB - Let Ks,t* denote the graph obtained from Ks, t by adding all edges between the s vertices of degree t in it. We show how to adapt the argument of our previous paper [A.V. Kostochka, N. Prince, On Ks, t-minors in graphs with given average degree, Discrete Math. 308 (2008) 4435-4445] to prove that if tlog 2t<1000s, then every graph G with average degree at least t+8slog 2s has a Ks,t* minor. This refines a corresponding result by Kühn and Osthus.

KW - Bipartite minors

KW - Dense graphs

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U2 - 10.1016/j.disc.2012.08.004

DO - 10.1016/j.disc.2012.08.004

M3 - Article

AN - SCOPUS:84867098991

VL - 312

SP - 3517

EP - 3522

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 24

ER -