Vertex-Disjoint Paths in Graphs

Yoshimi Egawa, Katsuhiro Ota

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let n1, n2, . . ., nk be integers of at least two. Johansson gave a minimum degree condition for a graph of order exactly n1 + n2 + ⋯ + nk to contain k vertex-disjoint paths of order n1, n2, . . ., nk, respectively. In this paper, we extend Johansson's result to a corresponding packing problem as follows. Let G be a connected graph of order at least n1 + n2 + ⋯ + nk. Under this notation, we show that if the minimum degree sum of three independent vertices in G is at least (formula presented) then G contains k vertex-disjoint paths of order n1, n2, . . ., nk, respectively, or else n1 = n2 = ⋯ = nk = 3, or k = 2 and n1 = n2 = odd. The graphs in the exceptional cases are completely characterized. In particular, these graphs have more than n1 + n2 + ⋯ + nk vertices.

Original languageEnglish
Pages (from-to)23-31
Number of pages9
JournalArs Combinatoria
Volume61
Publication statusPublished - 2001 Dec 1

ASJC Scopus subject areas

  • Mathematics(all)

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