Functionality of Box Intersection Graphs

Abstract

AbstractFunctionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In the present paper, we show that functionality is bounded for box intersection graphs in $$\mathbb {R}^1$$ R 1 , i.e. for interval graphs, and unbounded for box intersection graphs in $$\mathbb {R}^3$$ R 3 . We also study a parameter known as symmetric difference, which is intermediate between twin-width and functionality, and show that this parameter is unbounded both for interval graphs and for unit box intersection graphs in $$\mathbb {R}^2$$ R 2 .