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On the Chromatic Number of H-Free Graphs of Large Minimum Degree

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Abstract

The problem of determining the chromatic number of H-free graphs has been well studied, with particular attention to K r -free graphs with large minimum degree. Recent progress has been made for triangle-free graphs on n vertices with minimum degree larger than n/3. In this paper, we determine the family of r-colorable graphs \({\mathcal{H}_r}\), such that if \({H \in \mathcal{H}_r}\), there exists a constant C < (r − 2)/(r − 1) such that any H-free graph G on n vertices with δ(G) > Cn has chromatic number bounded above by a function dependent only on H and C. A value of C < (r − 2)/(r − 1) is given for every \({H \in \mathcal{H}_r}\), with particular attention to the case when χ(H) = 3.

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  1. Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS, USA

    Jeremy Lyle

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  1. Jeremy Lyle
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Lyle, J. On the Chromatic Number of H-Free Graphs of Large Minimum Degree. Graphs and Combinatorics 27, 741–754 (2011). https://doi.org/10.1007/s00373-010-0994-x

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  • DOI: https://doi.org/10.1007/s00373-010-0994-x

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