On Ks,t minors in (s+t)-chromatic graphs
نویسندگان
چکیده
منابع مشابه
Minors in Graphs with High Chromatic Number
THOMAS BÖHME, ALEXANDR KOSTOCHKA2† and ANDREW THOMASON 1Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany (e-mail: [email protected]) 2 Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Sobolev Institute of Mathematics, Novosibirsk, Russia (e-mail: [email protected]) 3 DPMMS, Centre for Mathematical Sciences, Wilberforce Road, ...
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Let K∗ s,t denote the graph obtained from the complete graph Ks+t by deleting the edges of some Kt -subgraph. We prove that for each fixed s and sufficiently large t, every graph with chromatic number s+t has a K∗ s,t minor. 2010 Wiley Periodicals, Inc. J Graph Theory 65: 343–350, 2010 MSC 2000: 05 C 15; 05 C 83
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Alexandr Kostochka In search of ways to attack Hadwiger’s Conjecture, Woodall and independently Seymour suggested to prove the weaker conjecture that Every (s + t)-chromatic graph has a Ks,t-minor. If the conjecture were true for all values of s and t, it would imply that for k ≥ 2 every (2k − 2)-chromatic graph has a Kk-minor. The conjecture is evident for s = 1. The validity of the conjecture...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2010
ISSN: 0364-9024
DOI: 10.1002/jgt.20485