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Hamiltonian graphs involving distances

✍ Scribed by Guantao Chen; R. H. Schelp

Publisher: John Wiley and Sons
Year: 1992
Tongue: English
Weight: 368 KB
Volume: 16
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190160203

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let G be a graph of order n. We show that if G is a 2‐connected graph and max{d(u), d(v)} + |N(u) U N(v)| ≥ n for each pair of vertices u, v at distance two, then either G is hamiltonian or G 3K~n/3~ U T~1~ U T~2~, where n  O (mod 3), and T~1~ and T~2~ are the edge sets of two vertex disjoint triangles containing exactly one vertex from each K~n/3~. This result generalizes both Fan's and Lindquester's results as well as several others.

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