Grounded L-graphs are polynomially χ-bounded

08/12/2021

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by   James Davies, et al.

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A grounded L-graph is the intersection graph of a collection of "L" shapes whose topmost points belong to a common horizontal line. We prove that every grounded L-graph with clique number ω has chromatic number at most 17ω^4. This improves the doubly-exponential bound of McGuinness and generalizes the recent result that the class of circle graphs is polynomially χ-bounded. We also survey χ-boundedness problems for grounded geometric intersection graphs and give a high-level overview of recent techniques to obtain polynomial bounds.