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arXiv · 2412.05891

A note on finding large transversals efficiently

Michael Anastos·Patrick Morris
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Abstract

In an $n \times n$ array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more than $βn$ times, the array contains a transversal of size $(1-β/4-o(1))n$. In particular, if the array is filled with $n$ symbols, each appearing $n$ times (an equi-$n$ square), we get transversals of size $(3/4-o(1))n$. Moreover, our proof gives a deterministic algorithm with polynomial running time, that finds these transversals.

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Michael Anastos, Patrick Morris. 2026-06-22. A note on finding large transversals efficiently. https://arxiv.org/abs/2412.05891

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