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Every connected, locally connected nontrivial graph with no induced claw is hamiltonian

✍ Scribed by David J. Oberly; Slobodan K. Simić; David P. Sumner

Publisher: John Wiley and Sons
Year: 1979
Tongue: English
Weight: 232 KB
Volume: 3
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190030405

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✦ Synopsis

Abstract

A graph is locally connected if every neighborthood induces a connected subgraph. We show here that every connected, locally connected graph on p ≥ 3 vertices and having no induced K~1,3~ is Hamiltonian. Several sufficient conditions for a line graph to be Hamiltonian are obtained as corollaries.

📜 SIMILAR VOLUMES

Every 3-connected claw-free Z8-free grap

Every 3-connected claw-free Z8-free graph is Hamiltonian

✍ Hong-Jian Lai; Liming Xiong; Huiya Yan; Jin Yan 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 115 KB 👁 2 views

## Abstract In this article, we first show that every 3‐edge‐connected graph with circumference at most 8 is supereulerian, which is then applied to show that a 3‐connected claw‐free graph without __Z__~8~ as an induced subgraph is Hamiltonian, where __Z__~8~ denotes the graph derived from identify