, Volume 20, Issue 3, pp 239–253 | Cite as

Decomposing Graphs into Long Paths

  • Alexandr Kostochka
  • Vladimir Tashkinov


It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C 3, C 4, C 5, and K 4e have no such decompositions. We construct an infinite sequence {F i } i=0 of nondecomposable graphs. On the other hand, we prove that every other 2-edge-connected graph has a desired decomposition.

edge-decompositions of graphs 2-edge-connected graphs 


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  1. 1.
    Li, W.: Problem 9.26, In: I. Rival (ed.), Graphs and Order, D. Reidel Publishing Co., Dordrecht, 1985.Google Scholar
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    Petersen, J.: Die Theorie der regulären Graphen, Acta Math. 15 (1891), 193–220.zbMATHCrossRefGoogle Scholar
  3. 3.
    West, D. B.: Introduction to Graph Theory, 2nd edn, Prentice-Hall, Upper Saddle River, 2001, Problem 3.3.20 on p. 147.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Alexandr Kostochka
    • 1
    • 2
  • Vladimir Tashkinov
    • 3
  1. 1.University of IllinoisUrbana, sUSA
  2. 2.Institute of MathematicsNovosibirskRussia
  3. 3.Institute of MathematicsNovosibirskRussia

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