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Cycle double covers and spanning minors IPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2006 (English)In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 96, no 2, 183-206 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

New York etc.: Academic Press , 2006. Vol. 96, no 2, 183-206 p.
##### Keyword [en]

Cycle double cover, Kotzig; Frame, Cubic graphs
##### Identifiers

URN: urn:nbn:se:umu:diva-7660DOI: 10.1016/j.jctb.2005.07.004OAI: oai:DiVA.org:umu-7660DiVA: diva2:147331
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Available from: 2008-01-11 Created: 2008-01-11 Last updated: 2011-04-08Bibliographically approved

Define a graph to be a Kotzig graph if it is $m$-regular and has an $m$-edge colouring in which each pair of colours form a Hamiltonian cycle. We show that every cubic graph with spanning subgraph consisting of a subdivision of a Kotzig graph together with even cycles has a cycle double cover, in fact a 6-CDC. We prove this for two other families of graphs similar to Kotzig graphs as well. In particular, let $F$ be a 2-factor in a cubic graph $G$ and denote by $G_{F}$ the pseudograph obtained by contracting each component in $F$. We show that if there exist a cycle in $G_{F}$ through all vertices of odd degree, then $G$ has a CDC. We conjecture that every 3-connected cubic graph contains a spanning subgraph homeomorphic to a Kotzig graph. In a sequel we show that every cubic graph with a spanning homeomorph of a 2-connected cubic graph on at most 10 vertices has a CDC.

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