Thresholds for classes of intersection graphs
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
Trapezoid graphs and generalizations, geometry and algorithms
Discrete Applied Mathematics
Permutation Graphs and Transitive Graphs
Journal of the ACM (JACM)
Maximum weight independent sets and cliques in intersection graphs of filaments
Information Processing Letters
Algorithms for maximum weight induced paths
Information Processing Letters
Maximum independent set and maximum clique algorithms for overlap graphs
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Minimum weight feedback vertex sets in circle graphs
Information Processing Letters
Algorithms on Subtree Filament Graphs
Graph Theory, Computational Intelligence and Thought
Algorithms for induced biclique optimization problems
Information Processing Letters
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
| Hi-index | 0.04 |
Gavril [F. Gavril, Maximum weight independent sets and cliques in intersection graphs of filaments, Inform. Process. Lett. 73 (2000) 181-188] defined two new families of intersection graphs: the interval-filament graphs and the subtree-filament graphs. The complements of interval-filament 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 generalization of the subtree-filament graphs, namely, the 3D-interval-filament graphs. We prove that the family of 3D-interval-filament graphs, the family of complements of co(interval-filament) mixed graphs and the family of overlap graphs of interval-filaments are the same, and show that every 3D-interval-filament graph has an intersection representation by a family of piecewise linear filaments. We use the properties of these graphs to describe an algorithm for maximum weight holes of a given parity in 3D-interval-filament graphs and an algorithm for antiholes of a given parity in interval-filament and subtree-filament graphs. We define various subfamilies of 3D-interval-filament graphs and characterize them as overlap graphs and as complements of H-mixed graphs.