Fan-type theorem for a long path passing through a specified vertex

Hikoe Enomoto, Jun Fujisawa

研究成果: Article

抄録

Let G be a 2-connected graph with maximum degree Δ(G) ≥ d, x and z be distinct vertices of G, and W be a subset of V (G)\{x, z} such that |W| ≤ d - 1. Hirohata proved that if max{dG(u), dG(v)} ≥ d for every pair of vertices u, v ∈ V(G)\({x,z} ∪ W) such that d G(u, v) = 2, then x and z are joined by a path of length at least d - |W|. In this paper, we show that if G satisfies the conditions of Hirohata's theorem, then for any given vertex y such that dG(y) ≥ d, x and z are joined by a path of length at least d - |W| which contains y.

本文言語English
ページ(範囲)129-136
ページ数8
ジャーナルArs Combinatoria
90
出版ステータスPublished - 2009 1 1

ASJC Scopus subject areas

  • Mathematics(all)

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