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Minimum k-hamiltonian graphs, II

✍ Scribed by M. Paoli; W. W. Wong; C. K. Wong

Publisher: John Wiley and Sons
Year: 1986
Tongue: English
Weight: 523 KB
Volume: 10
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190100111

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✦ Synopsis

We consider in this paper graphs which remain hamiltonian after the removal of k edges (k-edge hamiltonian) or k vertices (k-hamiltonian). These classes of graphs arise from reliability considerations in network design. In a previous paper, W. W. Wong and C. K. Wong presented families of minimum k-hamiltonian graphs and minimum k-edge hamiltonian graphs for k even. Here, w e complete this study in the case where k is odd.

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## Abstract For a positive integer __k__, a graph __G__ is __k‐ordered hamiltonian__ if for every ordered sequence of __k__ vertices there is a hamiltonian cycle that encounters the vertices of the sequence in the given order. It is shown that if __G__ is a graph of order __n__ with 3 ≤ __k__ ≤ __n