The paint pot problem and common multiples in monoids

Abstract Illustrated by a problem on paint pots that is easy to understand but hard solve, we investigate whether particular monoids have the property of common right multiples. As one result characterize generalized braid represented undirected graphs, being subclass Artin–Tits monoids. Stated in other words, which graphs old Garside stating multiples, generalizes. This characterization also follows from results Coxeter groups and connection between finiteness multiples However, our independent presentation self-contained up some basic knowledge rewriting, applies beyond format. The main new contribution technique prove does not hold, finding model, examples all finite.