Spanning 3-colourable subgraphs of small bandwidth in dense graphs

Authors:
Julia Böttcher;Mathias Schacht;Anusch Taraz
Affiliations:
Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747 Garching bei München, Germany;Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany;Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747 Garching bei München, Germany
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

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Abstract

A conjecture by Bollobas and Komlos states the following: For every@c0and integersr=2and @D, there exists@b0with the following property. If G is a sufficiently large graph with n vertices and minimum degree at least(r-1r+@c)nand H is an r-chromatic graph with n vertices, bandwidth at most @bn and maximum degree at most @D, then G contains a copy of H. This conjecture generalises several results concerning sufficient degree conditions for the containment of spanning subgraphs. We prove the conjecture for the case r=3.