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 -