Graph decompositions and D3-paths with a prescribed endvertex

Hikoe Enomoto, Shinsuke Matsunaga, Ota Katsuhiro

研究成果: Conference article

1 引用 (Scopus)

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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.)

元の言語English
ページ(範囲)87-104
ページ数18
ジャーナルDiscrete Mathematics
213
発行部数1-3
DOI
出版物ステータスPublished - 2000 2 28
イベントSelected Topics in Discrete Mathematics - Warsaw, Poland
継続期間: 1996 8 261996 9 28

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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