Skip to main content
Log in

On the Existence of a Long Path Between Specified Vertices in a 2-Connected Graph

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract.

 Let G be a 2-connected graph with maximum degree Δ (G)≥d, and let x and y be distinct vertices of G. Let W be a subset of V(G)−{x, y} with cardinality at most d−1. Suppose that max{d G(u), d G(v)}≥d for every pair of vertices u and v in V(G)−({x, y}∪W) with d G(u,v)=2. Then x and y are connected by a path of length at least d−|W|.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received: February 5, 1998 Revised: April 13, 1998

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hirohata, K. On the Existence of a Long Path Between Specified Vertices in a 2-Connected Graph. Graphs Comb 16, 269–273 (2000). https://doi.org/10.1007/PL00007222

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/PL00007222

Keywords

Navigation