Modular intersection graphs
A graph \(G=(V,E)\) is a modular intersection graph on a finite set \(U\) if there is a family of subsets \(S=\{S_x\mid x\in V\}\) of \(U\) and positive integers \(t<m\) such that \(\{x,y\}\) is an edge of \(G\) if and only if there is an integer \(r\) with \(t\leq r<m\) such that \(|S_x\cap S_y|\equiv r\pmod m\). The special cases considered include modular interval graphs (\(U\) is the vertex set of a path and each \(S_x\) is connected), modular subtree graphs (\(U\) is the vertex set of a tree and each \(S_x\) is connected), and parity intersection graphs (\(t=1\) and \(m=2\)).
scientific article; zbMATH DE number 934039
scientific article