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arXiv · 2603.21585

Computing the Girth of a Segment Intersection Graph

Timothy M. Chan·Yuancheng Yu
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Abstract

We present an algorithm that computes the girth of the intersection graph of $n$ given line segments in the plane in $O(n^{1.483})$ expected time. This is the first such algorithm with $O(n^{3/2-\varepsilon})$ running time for a positive constant $\varepsilon$, and makes progress towards an open question posed by Chan (SODA 2023). The main techniques include (i)~the usage of recent subcubic algorithms for bounded-difference min-plus matrix multiplication, and (ii)~an interesting variant of the planar graph separator theorem. The result extends to intersection graphs of connected algebraic curves or semialgebraic sets of constant description complexity.

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Timothy M. Chan, Yuancheng Yu. 2026-03-23. Computing the Girth of a Segment Intersection Graph. https://arxiv.org/abs/2603.21585

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