On directed local chromatic number,shift graphs,and Borsuk‐like graphs |
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Authors: | Gábor Simonyi Gábor Tardos |
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Institution: | 1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1364 Budapest, POB 127, Hungary;2. School of Computing Science, Simon Fraser University, Burnaby BC, Canada V5A 1S6 |
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Abstract: | We investigate the local chromatic number of shift graphs and prove that it is close to their chromatic number. This implies that the gap between the directed local chromatic number of an oriented graph and the local chromatic number of the underlying undirected graph can be arbitrarily large. We also investigate the minimum possible directed local chromatic number of oriented versions of “topologically t‐chromatic” graphs. We show that this minimum for large enough t‐chromatic Schrijver graphs and t‐chromatic generalized Mycielski graphs of appropriate parameters is ?t/4?+1. © 2010 Wiley Periodicals, Inc. J Graph Theory 66: 65‐82, 2010 |
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Keywords: | local chromatic number shift graph Schrijver graph topological method |
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