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On snarks that are far from being 3-edge colorable
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2016 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 23, no 2, P2.6Article in journal (Refereed) Published
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Text
Abstract [en]

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
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-123472ISI: 000377677300012OAI: oai:DiVA.org:umu-123472DiVA: diva2:949185
Available from: 2016-07-18 Created: 2016-07-04 Last updated: 2016-07-18Bibliographically approved

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