Document Type
Article
Publication Date
2011
Publication Title
The Electronic Journal of Combinatorics
ISSN
1077-8926
Abstract
We show that, in a k-connected graph G of order n with α(G)=α, between any pair of vertices, there exists a path P joining them with
|P|≥min{n,(k−1)(n−k)/α +k}.
This implies that, for any edge e∈E(G), there is a cycle containing e of length at least
min{n,(k−1)(n−k)/α +k}.
Moreover, we generalize our result as follows: for any choice S of s≤k vertices in G, there exists a tree T whose set of leaves is S with
|T|≥min{n,(k−s+1)(n−k)/α +k}.
Recommended Citation
Fujita, Shinya, Alexander Halperin, Colton Magnant.
2011.
"Long Path Lemma Concerning Connectivity and Independence Number."
The Electronic Journal of Combinatorics, 18 (1).
source: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p149
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/116
Comments
Copyright of the article remains with the author. Article obtained from the Electronic Journal of Combinatorics.