Partitions of a graph into paths with prescribed endvertices and lengths

Hikoe Enomoto, Katsuhiro Ota

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

For a graph G, let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| = n = Σki=1 ai and σ2(G) ≥ n+k - 1, then for any k vertices v1, v2, . . . , vk in G, there exist vertex-disjoint paths P1, P2, . . ., Pk such that | V(Pi)| = ai and vi is an endvertex of Pi for 1 ≤i≤ k. In this paper, we verify the conjecture for the cases where almost all ai≤5, and the cases where k≤3.

Original languageEnglish
Pages (from-to)163-169
Number of pages7
JournalJournal of Graph Theory
Volume34
Issue number2
DOIs
Publication statusPublished - 2000 Jun

ASJC Scopus subject areas

  • Geometry and Topology

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