Generating p-extremal graphs
Abstract
Define f(n,p) to be the maximum number of edges in a graph on n vertices with p perfect matchings. Dudek and Schmitt proved there exist constants n_p and c_p so that for even n >= n_p, f(n,p) = (n^2)/4+c_p. A graph is p-extremal if it has p perfect matchings and (n^2)/4+c_p edges. Based on Lovasz's Two Ear Theorem and structural results of Hartke, Stolee, West, and Yancey, we develop a computational method for determining c_p and generating the finite set of graphs which describe the infinite family of p-extremal graphs. This method extends the knowledge of the size and structure of p-extremal graphs from p <= 10 to p <= 27. These values provide further evidence towards a conjectured upper bound and prove the sequence c_p is not monotonic.
Keywords
Cite
@article{arxiv.1105.1764,
title = {Generating p-extremal graphs},
author = {Derrick Stolee},
journal= {arXiv preprint arXiv:1105.1764},
year = {2011}
}
Comments
25 pages, 2 figures, 3 tables