Maximal skew sets of lines on a Hermitian surface and a modified Bron-Kerbosch algorithm

Anna Brosowsky; Haoyu Du; Madhav Krishna; Sandra Nair; Janet Page; Tim Ryan

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arXiv · 2211.16580

Maximal skew sets of lines on a Hermitian surface and a modified Bron-Kerbosch algorithm

Anna Brosowsky·Haoyu Du·Madhav Krishna·Sandra Nair·Janet Page·Tim Ryan

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Abstract

In this paper, we study maximal sets of skew lines on Hermitian surfaces. We give a new algorithm to compute these sets and give some computational results for Hermitian surfaces of degrees 3,4, and 5. In more generality, this algorithm solves a new variant of the clique listing problem, which may be more approachable than the classical problem. Finally, we explicitly construct a large skew set of lines on Hermitian varieties of any degree and use it to give a lower bound on the largest size of maximal skew sets and a lower bound on the possible number of maximal skew sets.

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Anna Brosowsky, Haoyu Du, Madhav Krishna, Sandra Nair, Janet Page, Tim Ryan. 2022-11-29. Maximal skew sets of lines on a Hermitian surface and a modified Bron-Kerbosch algorithm. https://arxiv.org/abs/2211.16580

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