Coloring triangle-free L-graphs with $O(\log\log n)$ colors

TL;DR

This paper proves that triangle-free intersection graphs of L-shapes in the plane can be colored with O(log log n) colors, significantly improving previous bounds and matching known lower bounds.

Contribution

It establishes a tighter upper bound of O(log log n) for coloring triangle-free L-graph intersection graphs, advancing understanding of their chromatic properties.

Findings

Triangle-free L-graph intersection graphs are O(log log n) colorable.

Improves previous O(log n) bound to O(log log n).

Matches the known lower bound for such graphs.

Abstract

It is proved that triangle-free intersection graphs of $n$ L-shapes in the plane have chromatic number $O(\log\log n)$. This improves the previous bound of $O(\log n)$ (McGuinness, 1996) and matches the known lower bound construction (Pawlik et al., 2013).