On snarks that are far from being 3-edge colorable
2016 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 23, no 2, P2.6Article in journal (Refereed) PublishedText
In this note we construct two infinite snark families which have high oddness and low circumference compared to the number of vertices. Using this construction, we also give a counterexample to a suggested strengthening of Fulkerson's conjecture by showing that the Petersen graph is not the only cyclically 4-edge connected cubic graph which require at least five perfect matchings to cover its edges. Furthermore the counterexample presented has the interesting property that no 2-factor can be part of a cycle double cover.
Place, publisher, year, edition, pages
2016. Vol. 23, no 2, P2.6
IdentifiersURN: urn:nbn:se:umu:diva-123472ISI: 000377677300012OAI: oai:DiVA.org:umu-123472DiVA: diva2:949185