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Bounding the Distance Among Longest Paths in a Connected Graph by Ekstein, Jan; Fujita, Shinya; Kabela, Adam; Teska, Jakub is a scholarly article available to read on EtoBox.

What is Bounding the Distance Among Longest Paths in a Connected Graph about?

It is easy to see that in a connected graph any 2 longest paths have a vertex in common. For k>=7, Skupien in [7] obtained a connected graph in which some k longest paths have no common vertex, but every k-1 longest paths have a common vertex. It is not known whether every 3 longest paths in a connected graph have a common vertex and similarly for 4, 5, and 6 longest path. In [5] the authors give an upper bound on distance among 3 longest paths in a connected graph. In this paper we give a similar upper bound on distance between 4 longest paths and also for k longest paths, in general.

Author

Ekstein, Jan; Fujita, Shinya; Kabela, Adam; Teska, Jakub

Published

2016

Language

EN