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Pk+1-Decompositions of Eulerian Graphs: Complexity and Some Solvable CasesPrimeFaces.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}); 2003 (English)In: Electronic Notes in Discrete Mathematics, ISSN 1571-0653, Vol. 13Article in journal (Refereed) Published
##### Abstract [en]

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

2003. Vol. 13
##### Keyword [en]

eulerian graph, NP-complete, path decomposition, pendant triangle
##### National Category

Engineering and Technology
##### Identifiers

URN: urn:nbn:se:liu:diva-46685DOI: 10.1016/S1571-0653(04)00426-3OAI: oai:DiVA.org:liu-46685DiVA: diva2:267581
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Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-13

We consider the problem of PMk+1-decomposition of a simple eulerian graph G, that is, decomposition of G into edge disjoint paths of length k. We show that the problem of deciding whether there exists a Pk+1 - decomposition of an eulerian simple graph is NP-complete, for every k = 3. However we find some new classes of graphs where the problem of P4-decomposition can be solved polynomially. We show that an eulerian simple graph G on 3m = 6 edges admits a P4-decomposition if G has no cut vertex v such that exactly one of the components in the graph G - ? has two vertices. In particular, this implies that a 2-connected eulerian simple graph G on 3m = 6 edges admits a P4 -decomposition. © 2003.

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