2005•Journal of Graph TheoryRequires access

Constructions of bipartite graphs from finite geometries

Keith E. Mellinger, Dhruv Mubayi

Abstract

Abstract We construct an incidence structure using certain points and lines in finite projective spaces. The structural properties of the associated bipartite incidence graphs are analyzed. These n × n bipartite graphs provide constructions of C6‐free graphs with Ω(n4/3 edges, C10‐free graphs with Ω(n6/5) edges, and Θ(7,7,7)‐free graphs with Ω(n8/7) edges. Each of these bounds is sharp in order of magnitude. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 1–10, 2005

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Key concepts: Mathematics, Bipartite graph, Combinatorics, Cograph, Discrete mathematics, 1-planar graph, Indifference graph, Pathwidth