Graph decompositions and D3-paths with a prescribed endvertex

Hikoe Enomoto, Shinsuke Matsunaga, Ota Katsuhiro

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)


Let k and n be positive integers. Let G be a graph of order n≤4k, and let n = ∑ki=1 ai be a partition of n into k positive integers ai with 1≤ai≤4. In Matsunaga (Preprint, 1995) one of the authors proved that if G is 2-connected and the minimum degree of G is at least k, then with certain types of exceptions being allowed, the vertex set of G can be decomposed into k disjoint subsets Al,...,Ak so that |Ai| = ai and "the subgraph induced by Ai is connected" for all i, 1≤i≤k. In the present paper we extend this result for connected graphs in general. The paper also features the existence of D3-paths with a prescribed endvertex in a graph. (A D3-path in a graph is a path of the graph whose removal leaves no component of order at least 3.)

Original languageEnglish
Pages (from-to)87-104
Number of pages18
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - 2000 Feb 28
EventSelected Topics in Discrete Mathematics - Warsaw, Poland
Duration: 1996 Aug 261996 Sept 28


  • D-path
  • Graph decomposition

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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