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- W1611704200 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." @default.
- W1611704200 created "2016-06-24" @default.
- W1611704200 creator A5000119939 @default.
- W1611704200 date "2011-05-09" @default.
- W1611704200 modified "2023-09-27" @default.
- W1611704200 title "Generating p-extremal graphs" @default.
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