Discussiones Mathematicae Graph Theory 24(1) (2004) 115-123
DOI: https://doi.org/10.7151/dmgt.1218
A NOTE ON MINIMALLY 3-CONNECTED GRAPHS
Víctor Neumann-Lara
Instituto de Matemáticas |
Eduardo Rivera-Campo
Departamento de Matemáticas |
Jorge Urrutia
Instituto de Matemáticas |
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