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Smallest Sets of Longest Paths with Empty Intersection

Published online by Cambridge University Press:  12 September 2008

Z. Skupień
Z. Skupień
Affiliation:
Technical University, WSI, Zielona Góra, Poland
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Abstract

It is shown that, for every integer v < 7, there is a connected graph in which some v longest paths have empty intersection, but any v – 1 longest paths have a vertex in common. Moreover, connected graphs having seven or five minimal sets of longest paths (longest cycles) with empty intersection are presented. A 26-vertex 2-connected graph whose longest paths have empty intersection is exhibited.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 429 - 436
Copyright
Copyright © Cambridge University Press 1996

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