A note on the girth of digraphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1982 English Publisher:Springer Science and Business Media LLCJournal:Combinatorica, volume 2, pages 143-147 (issn: 0209-9683, eissn: 1439-6912,

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Authors: Yahya Ould Hamidoune;

doi: 10.1007/bf02579312

A note on the girth of digraphs

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Abstract

Behzad, Chartrand and Wall conjectured that the girth of a diregular graph of ordern and outdegreer is not greater than [n /r]. This conjecture has been proved forr=2 by Behzad and forr=3 by Bermond. We prove that a digraph of ordern and halfdegree ≧4 has girth not exceeding [n / 4]. We also obtain short proofs of the above results. Our method is an application of the theory of connectivity of digraphs.

Related Organizations

Sorbonne Université
France
Sorbonne University
France

Keywords

girth, Extremal problems in graph theory, Connectivity, Directed graphs (digraphs), tournaments, diregular graph

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