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On the line-connectivity of line-graphs

✍ Scribed by Tudor Zamfirescu

Publisher: Springer
Year: 1970
Tongue: English
Weight: 193 KB
Volume: 187
Category: Article
ISSN: 0025-5831
DOI: 10.1007/bf01396460

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A well-known conjecture of Thomassen says that every 4-connected line graph is hamiltonian. In this paper we prove that every 7-connected line graph is hamiltonian-connected. For line graph, C. Thomassen [l] made the following conjecture. Conjecture. Every 4-connected line graph is hamiltonian.

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## Abstract Let __G__ be a graph and let __V__~0~ = {ν∈ __V__(__G__): __d__~__G__~(ν) = 6}. We show in this paper that: (i) if __G__ is a 6‐connected line graph and if |__V__~0~| ≤ 29 or __G__[__V__~0~] contains at most 5 vertex disjoint __K__~4~'s, then __G__ is Hamilton‐connected; (ii) every 8‐co