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Incidence Posets and Cover Graphs

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Abstract

We prove two theorems concerning incidence posets of graphs, cover graphs of posets and a related graph parameter. First, answering a question of Haxell, we show that the chromatic number of a graph is not bounded in terms of the dimension of its incidence poset, provided the dimension is at least four. Second, answering a question of Kříž and Nešetřil, we show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most two.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    William T. Trotter & Ruidong Wang

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  1. William T. Trotter
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  2. Ruidong Wang
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Correspondence to William T. Trotter.

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Trotter, W.T., Wang, R. Incidence Posets and Cover Graphs. Order 31, 279–287 (2014). https://doi.org/10.1007/s11083-013-9301-9

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  • DOI: https://doi.org/10.1007/s11083-013-9301-9

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