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Bichain graphs : Geometric model and universal graphs
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Brignall, Robert, Lozin, Vadim V. and Stacho, Juraj (2016) Bichain graphs : Geometric model and universal graphs. Discrete Applied Mathematics, 199 . pp. 16-29. doi:10.1016/j.dam.2014.08.031 ISSN 0166-218X.
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Official URL: http://dx.doi.org/10.1016/j.dam.2014.08.031
Abstract
Bichain graphs form a bipartite analog of split permutation graphs, also known as split graphs of Dilworth number 2. Unlike graphs of Dilworth number 1 that enjoy many nice properties, split permutation graphs are substantially more complex. To better understand the global structure of split permutation graphs, in the present paper we study their bipartite analog. We show that bichain graphs admit a simple geometric representation and have a universal element of quadratic order, i.e. an -universal bichain graph with vertices. The latter result improves a recent cubic construction of universal split permutation graphs.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Discrete Applied Mathematics | ||||
Publisher: | Elsevier Science Ltd. | ||||
ISSN: | 0166-218X | ||||
Official Date: | January 2016 | ||||
Dates: |
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Volume: | 199 | ||||
Page Range: | pp. 16-29 | ||||
DOI: | 10.1016/j.dam.2014.08.031 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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