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COMBINATORICS
2006

Bounding the Number of Edges in Permutation Graphs

8 years 11 months ago
Bounding the Number of Edges in Permutation Graphs
Given an integer s 0 and a permutation Sn, let ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and there are at most s integers k, i < k < j, such that = [. . . j . . . k . . . i . . .]. In this short paper we determine the maximum number of edges in ,s for all s 1 and characterize all permutations which achieve this maximum. This answers an open question of Adin and Roichman, who studied the case s = 0. We also consider another (closely related) permutation graph, defined by Adin and Roichman, and obtain asymptotically tight bounds on the maximum number of edges in it.
Peter Keevash, Po-Shen Loh, Benny Sudakov
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Peter Keevash, Po-Shen Loh, Benny Sudakov
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