# Mácajová and Škoviera conjecture on cubic graphs

Jean-Luc Fouquet; Jean-Marie Vanherpe

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 2, page 315-333
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topJean-Luc Fouquet, and Jean-Marie Vanherpe. "Mácajová and Škoviera conjecture on cubic graphs." Discussiones Mathematicae Graph Theory 30.2 (2010): 315-333. <http://eudml.org/doc/271076>.

@article{Jean2010,

abstract = {A conjecture of Mácajová and Skoviera asserts that every bridgeless cubic graph has two perfect matchings whose intersection does not contain any odd edge cut. We prove this conjecture for graphs with few vertices and we give a stronger result for traceable graphs.},

author = {Jean-Luc Fouquet, Jean-Marie Vanherpe},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Cubic graph; edge-partition; traceable graphs; cubic graph},

language = {eng},

number = {2},

pages = {315-333},

title = {Mácajová and Škoviera conjecture on cubic graphs},

url = {http://eudml.org/doc/271076},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Jean-Luc Fouquet

AU - Jean-Marie Vanherpe

TI - Mácajová and Škoviera conjecture on cubic graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 2

SP - 315

EP - 333

AB - A conjecture of Mácajová and Skoviera asserts that every bridgeless cubic graph has two perfect matchings whose intersection does not contain any odd edge cut. We prove this conjecture for graphs with few vertices and we give a stronger result for traceable graphs.

LA - eng

KW - Cubic graph; edge-partition; traceable graphs; cubic graph

UR - http://eudml.org/doc/271076

ER -

## References

top- [1] J.A. Bondy and U.S.R. Murty, Graph Theory, volume 244 of Graduate Text in Mathematics (Springer, 2008).
- [2] J. Edmonds, Maximum matching and a polyhedron with (0,1) vertices, J. Res. Nat. Bur. Standards (B) 69 (1965) 125-130. Zbl0141.21802
- [3] G. Fan and A. Raspaud, Fulkerson's conjecture and circuit covers, J. Combin. Theory (B) 61 (1994) 133-138, doi: 10.1006/jctb.1994.1039. Zbl0811.05053
- [4] J.L. Fouquet and J.M. Vanherpe, On Fan Raspaud Conjecture, manuscript, 2008.
- [5] D.R. Fulkerson, Blocking and anti-blocking pairs of polyhedra, Math. Programming 1 (1971) 168-194, doi: 10.1007/BF01584085. Zbl0254.90054
- [6] T. Kaiser, D. Král and S. Norine, Unions of perfect matchings in cubic graphs, Electronic Notes in Discrete Math. 22 (2005) 341-345, doi: 10.1016/j.endm.2005.06.079. Zbl1200.05172
- [7] T. Kaiser and A. Raspaud, Non-intersecting perfect matchings in cubic graphs, Electronic Notes in Discrete Math. 28 (2007) 293-299, doi: 10.1016/j.endm.2007.01.042. Zbl1291.05158
- [8] E. Màcajová and M. Skoviera, Fano colourings of cubic graphs and the Fulkerson conjecture, Theor. Comput. Sci. 349 (2005) 112-120, doi: 10.1016/j.tcs.2005.09.034. Zbl1082.05040
- [9] E. Màcajová and M. Skoviera, http://garden.irmacs.sfu.ca/?q=op/intersecting two perfect matchings, 2007.
- [10] P. Seymour, On multi-colourings of cubic graphs, and conjectures of Fulkerson and Tutte, Proc. London Math. Soc. 38 (1979) 423-460, doi: 10.1112/plms/s3-38.3.423. Zbl0411.05037

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.