Pk+1-Decompositions of Eulerian Graphs: Complexity and Some Solvable Cases
2003 (English)In: Electronic Notes in Discrete Mathematics, ISSN 1571-0653, Vol. 13Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2003. Vol. 13
eulerian graph, NP-complete, path decomposition, pendant triangle
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-46685DOI: 10.1016/S1571-0653(04)00426-3OAI: oai:DiVA.org:liu-46685DiVA: diva2:267581