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Edge-hamiltonian property in regular 2- connected graphs

✍ Scribed by Hao Li


Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
515 KB
Volume
82
Category
Article
ISSN
0012-365X

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✦ Synopsis


Bill Jackson has proved that every 2-connected, k-regular graph on at most 3k vertices is hamiltonian.

It is shown in this paper that, under almost the same conditions as above, the graphs are edge-hamiltonian.


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## Abstract Let Ξ³(__G__) be the domination number of graph __G__, thus a graph __G__ is __k__‐edge‐critical if Ξ³ (__G__) = k, and for every nonadjacent pair of vertices __u__ and Ο…, Ξ³(__G__ + __u__Ο…) = kβˆ’1. In Chapter 16 of the book β€œDomination in Graphsβ€”Advanced Topics,” D. Sumner cites a conjectu