A Turan-type problem on distances in graphs
Combinatorics
2012-08-09 v2
Abstract
We suggest a new type of problem about distances in graphs and make several conjectures. As a first step towards proving them, we show that for sufficiently large values of n and k, a graph on n vertices that has no three vertices at pairwise distance k has at most (n-k+1)^2/4 pairs of vertices at distance k.
Keywords
Cite
@article{arxiv.1011.2450,
title = {A Turan-type problem on distances in graphs},
author = {Mykhaylo Tyomkyn and Andrew Uzzell},
journal= {arXiv preprint arXiv:1011.2450},
year = {2012}
}
Comments
16 pages, 7 figures. Corrected errors and added several details to proof of main result