Mácajová and Škoviera conjecture on cubic graphs

• Autorzy: Jean-Luc Fouquet , Jean-Marie Vanherpe
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Cubic graph; edge-partition; traceable graphs

Kategorie tematyczne

• 05C30: Enumeration in graph theory
• 05C70: Factorization, matching, partitioning, covering and packing

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 2
• Strony: 315-333

Daty

wydano

2010

otrzymano

2008-12-31

poprawiono

2009-09-12

zaakceptowano

2009-11-09

Twórcy

autor

Jean-Luc Fouquet

• L.I.F.O., Faculté des Sciences, B.P. 6759, Université d'Orléans, 45067 Orléans Cedex 2, France

autor

Jean-Marie Vanherpe

• L.I.F.O., Faculté des Sciences, B.P. 6759, Université d'Orléans, 45067 Orléans Cedex 2, France

Bibliografia

• [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.
• [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.
• [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.
• [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.
• [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.
• [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.
• [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.

Identyfikatory

DOI

10.7151/dmgt.1496