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An Extremal Characterization of the Incidence Graphs of Projective Planes

An Extremal Characterization of the Incidence Graphs of Projective Planes Let G be a 4-cycle free, bipartite graph on 2n vertices with partitions of equal cardinality n. Let c6(G) denote the number of cycles of length 6 in G. We prove that for n ≥ 3, c6(G) ≤ $$\frac{1} {3}\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)(n - r_n ) $$ , where $$r_n = \frac{1} {2} + \frac{{\sqrt {4n - 3} }} {2} $$ , with equality if and only if G is the incidence point-line graph of a projective plane. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

An Extremal Characterization of the Incidence Graphs of Projective Planes

Fiorini, Gene; Lazebnik, Felix
Acta Applicandae Mathematicae , Volume 52 (3) – Oct 13, 2004
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References (8)

Publisher
Springer Journals
Copyright
Copyright © 1998 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1005987814905
Publisher site
See Article on Publisher Site

Abstract

Let G be a 4-cycle free, bipartite graph on 2n vertices with partitions of equal cardinality n. Let c6(G) denote the number of cycles of length 6 in G. We prove that for n ≥ 3, c6(G) ≤ $$\frac{1} {3}\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)(n - r_n ) $$ , where $$r_n = \frac{1} {2} + \frac{{\sqrt {4n - 3} }} {2} $$ , with equality if and only if G is the incidence point-line graph of a projective plane.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Oct 13, 2004

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