Homomorphisms of planar signed graphs to signed projective cubes - Archive ouverte HAL
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2013

Homomorphisms of planar signed graphs to signed projective cubes

Abstract

We conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is bipartite and planar, admits a homomorphism to the signed projective cube of dimension 2g1. Our main result is to show that for a given g, this conjecture is equivalent to the corresponding case (k = 2g) of a conjecture of Seymour claiming that every planar k-regular multigraph with no odd edge-cut of less than k edges is k-edge-colorable. To this end, we exhibit several properties of signed projective cubes and establish a folding lemma for planar even signed graphs.
Fichier principal
Vignette du fichier
dmtcs_nrs_rev.pdf (147.72 Ko) Télécharger le fichier
Origin Publisher files allowed on an open archive

Dates and versions

hal-00876298 , version 1 (24-10-2013)
hal-00876298 , version 2 (28-03-2014)

Identifiers

Cite

Reza Naserasr, Edita Rollova, Eric Sopena. Homomorphisms of planar signed graphs to signed projective cubes. Discrete Mathematics and Theoretical Computer Science, 2013, Vol. 15 no. 3 (3), pp.1-12. ⟨10.46298/dmtcs.612⟩. ⟨hal-00876298v1⟩
231 View
1058 Download

Altmetric

Share

More