Graphs of prescribed girth and bi-degree
type: Item
instance of: scholarly article
title: Graphs of prescribed girth and bi-degree
zbMATH Open document ID: 0828.05034
author: Felix Lazebnik
author: V. A. Ustimenko
author: Zoltán Füredi
author: Ákos Seress
author: Andrew J. Woldar
published in: Journal of Combinatorial Theory. Series B
publication date: 1995-09-20T00:00:00Z
review text: A bipartite graph \(\Gamma(V_1\cup V_2, E)\) is said to have bi- degree \(r\), \(s\) if every vertex from \(V_1\) has degree \(r\) and every vertex from \(V_2\) has degree \(s\). \(\Gamma\) is called an \((r, s, t)\)- graph if, additionally, the girth of \(\Gamma\) (i.e. the length of a shortest cycle of \(\Gamma\)) is \(2t\). For \(t> 3\), very few examples of \((r, s, t)\)-graphs are known. In this paper, we give a recursive construction of \((r, s, t)\)-graphs for all \(r, s, t\geq 2\), as well as an algebraic construction of such graphs for all \(r, s\geq t\geq 3\).
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 798748
zbMATH Keywords: semi-Moore graphs
zbMATH Keywords: biregular graphs
zbMATH Keywords: bipartite graph
zbMATH Keywords: bi-degree
zbMATH Keywords: girth
MaRDI profile type: Publication
full work available at URL: jctb.1995.1033
OpenAlex ID: W2051411864
DOI: 10.1006/JCTB.1995.1033
description: scientific article; zbMATH DE number 798748