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Let ▫$G$▫ be an intersection graph of ▫$n$▫ geometric objects in the plane. We show that a maximum matching in ▫$G$▫ can be found in ▫$O(\rho^{3\omega/2}n^{\omega/2})$▫ time with high probability, where ▫$\rho$▫ is the density of the geometric objects and ▫$\omega>2$▫ is a constant such that ▫$n \ti ...

The concept of avoidable paths in graphs was introduced by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2019 as a common generalization of avoidable vertices and simplicial paths. In 2020, Bonamy, Defrain, Hatzel, and Thiebaut proved that every graph containing an induced path of order k ...