3D-interval-filament graphs

Gavril [GA4] defined two new families of intersection graphs: the interval-filament graphs and the subtree-filament graphs. The complements of intervalfilament graphs are the cointerval mixed graphs and the complements of subtree-filament graphs are the cochordal mixed graphs. The family of interval-filament graphs contains the families of cocomparability, polygon-circle, circle and chordal graphs. In the present paper we introduce a new family of intersection graphs, the 3Dinterval-filament graphs, which are a generalization of the subtree-filament graphs. We prove that the family of complements of 3D-interval-filament graphs is exactly the family of co(interval-filament) mixed graphs and every 3D-interval-filament graph has an intersection representation by a family of piecewise linear filaments. We define various subfamilies of 3D-interval-filament graphs characterized as complements of families of Gmixed graphs.