Abstract
We show that any cubic bridgeless graph with m edges contains two perfect matchings that cover at least 3m/5 edges, and three perfect matchings that cover at least 27m/35 edges.
Supported by the project 1M0545 and the Research Plan MSM 4977751301 of the Czech Ministry of Education.
The author was a postdoctoral Institute for Mathematics, Technical University Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany within the framework of the European training network COMBSTRU from October 2004 to July 2005. At the present, the author is a Fulbright scholar at School of Mathematics, Georgia Institute of Technology, 686 Cherry St, Atlanta, GA 30332-0160.
This author was partially supported by NSF Grant No. 0200595.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Diestel, Graph Theory, Springer, New York, 2000.
J. Edmonds, Maximum matching and a polyhedron with (0, l)-vertices, J. Res. Nat. Bur. Standards B 69 (1965), 125–130.
D. R. Fulkerson, Blocking and antiblocking pairs of polyhedra, Math. Programming 1 (1971), 168–194.
E. R. Scheinerman, D. H. Ullman, Fractional Graph Theory: A Rational Approach to the Theory of Graphs, John Wiley & Sons, Hoboken, 1997.
P. D. Seymour, On multi-colourings of cubic graphs, and conjectures of Fulkerson and Tutte, Proc. London Math. Soc. (3) 38 (1979), 423–460.
A. Schrijver, Combinatorial Optimization, Springer, New York, 2003.
C.-Q. Zhang, Integer Flows and Cycle Covers of Graphs, Dekker, New York, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kaiser, T., Král’, D., Norine, S. (2006). Unions of Perfect Matchings in Cubic Graphs. In: Klazar, M., Kratochvíl, J., Loebl, M., Matoušek, J., Valtr, P., Thomas, R. (eds) Topics in Discrete Mathematics. Algorithms and Combinatorics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33700-8_14
Download citation
DOI: https://doi.org/10.1007/3-540-33700-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33698-3
Online ISBN: 978-3-540-33700-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)