DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 24(1) (2004) 115-123
DOI: 10.7151/dmgt.1218

A NOTE ON MINIMALLY 3-CONNECTED GRAPHS

Víctor Neumann-Lara

Instituto de Matemáticas
Universidad Nacional Autónoma de México
Ciudad Universitaria, México D.F. 04510

Eduardo Rivera-Campo

Departamento de Matemáticas
Universidad Autónoma Metropolitana-Iztapalapa
Av. San Rafael Atlixco 186, México D.F. 09340

Jorge Urrutia

Instituto de Matemáticas
Universidad Nacional Autónoma de México
Ciudad Universitaria, México D.F. 04510

Abstract

If G is a minimally 3-connected graph and C is a double cover of the set of edges of G by irreducible walks, then | E(G)| ≥ 2| C| − 2.

Keywords: minimally 3-connected, walk double cover.

2000 Mathematics Subject Classification: 05C70, 05C38.

References

[1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (North Holland, 1981).
[2] R. Halin, Untersuchungen über minimale n-fach zusammenhängende Graphen, Math. Ann. 182 (1969) 175-188, doi: 10.1007/BF01350321.
[3] W. Mader, Minimale n-fach zusammenhängende Graphen mit maximaler Kantenzahl, J. Reine Angew. Math. 249 (1971) 201-207, doi: 10.1515/crll.1971.249.201.

Received 26 February 2002
Revised 13 November 2002