Bichain graphs: geometric model and universal graphs

Brignall, Robert; Lozin, Vadim V. and Stacho, Juraj (2016). Bichain graphs: geometric model and universal graphs. Discrete Applied Mathematics, 199 pp. 16–29.

DOI: https://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 n-universal bichain graph with n² vertices. The latter result improves a recent cubic construction of universal split permutation graphs.

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About

• Item ORO ID
• 40985
• Item Type
• Journal Item
• ISSN
• 0166-218X
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Infinite Antichains of Combinatorial Structures	EP/J006130/1	EPSRC (Engineering and Physical Sciences Research Council)

• Keywords
• intersection graph; universal graph; split permutation graph
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2014 Elsevier B.V
• Depositing User
• Robert Brignall