Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T19:42:20.082Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Voss, H.-J. (1991) Cycles and Bridges in Graphs. Deutscher Verlag Wiss.Google Scholar
[2]Zamfirescu, T. (1975) L'histoire et l'etat present des bornes connues pour Pkj, Ckj, P¯kj et C¯kj. Colloque sur la Théorie des Graphes (Paris 1974). Cahiers Centre Études Rech. Opér. 17 (2–4) 427–439.Google Scholar
[3]Ore, O. (1962) Theory of Graphs. AMS Colloq. Publ. 38. Providence, RI.Google Scholar
[4]Zamfirescu, T. (1993) Talk presented at Nový Smokovec (Slovakia) Conference.Google Scholar
[5]Skupień, Z. (1984) Homogeneously traceable and Hamiltonian connected graphs. Demonstratio Math. 17 1051–1067.Google Scholar
[6]Jendrol, S. and Skupień, Z. (1996) Exact numbers of longest cycles with empty intersection. Euro. J. Combin. In press.Google Scholar
[7]Zamfirescu, T. (1976) On longest paths and circuits in graphs. Math. Scand. 38 211–239.CrossRefGoogle Scholar