On bounding the chromatic number of L-graphs

Abstract We show that the intersection graph of a collection of subsets of the plane, where each subset forms an “L” shape whose vertical stem is infinite, has its chromatic number χ bounded by a function of the order of its largest clique ω, where it is shown that χ⩽2 ( 14 3 )(4 ω−1 −1) . This proves a special case of a conjecture of Gyarfas and Lehel.