A New Approach Towards a Conjecture on Intersecting Three Longest Paths
Combinatorics
2015-07-28 v2
Abstract
In 1966, T. Gallai asked whether every connected graph has a vertex that appears in all longest paths. Since then this question has attracted much attention and many work has been done in this topic. One important open question in this area is to ask whether any three longest paths contains a common vertex in a connected graph. It was conjectured that the answer to this question is positive. In this paper, we propose a new approach in view of distances among longest paths in a connected graph, and give a substantial progress towards the conjecture along the idea.
Keywords
Cite
@article{arxiv.1503.01219,
title = {A New Approach Towards a Conjecture on Intersecting Three Longest Paths},
author = {Shinya Fujita and Michitaka Furuya and Reza Naserasr and Kenta Ozeki},
journal= {arXiv preprint arXiv:1503.01219},
year = {2015}
}
Comments
11pages, 5figures