Abstract We prove a regularity result for minimal configurations of variational problems involving both bulk and surface energies in some bounded open region $$\varOmega \subseteq {\mathbb {R}}^n$$ Ω ⊆ R n . will ...

A graph is called $P_t$-free if it does not contain a $t$-vertex path as an induced subgraph. While $P_4$-free graphs are exactly cographs, the structure of for $t \geqslant 5$ remains little understood. On one hand, classic computational problems such Maximum Weight Independent Set (MWIS) and $3$-Coloring known to be NP-hard on any fixed $t$. other despite significant effort, polynomial-time a...