A study on two geometric location problems
Information Processing Letters
Containment graphs, posets, and related classes of graphs
Proceedings of the third international conference on Combinatorial mathematics
The max clique problem in classes of string-graphs
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
Covering and coloring polygon-circle graphs
Discrete Mathematics
Graph classes: a survey
Maximum weight independent sets and cliques in intersection graphs of filaments
Information Processing Letters
Minimum vertex cover in rectangle graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Minimum vertex cover in rectangle graphs
Computational Geometry: Theory and Applications
Towards a comprehensive theory of conflict-tolerance graphs
Discrete Applied Mathematics
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We give polynomial time algorithms for the maximum independent set and maximum clique problems for classes of overlap graphs, assuming an overlap model is provided as input. The independent set algorithm applies to any class of overlap graphs for which the maximum weight independent set problem is polynomially solvable on the corresponding intersection graph class, where the vertex weights are nonnegative integers on which arithmetic operations can be performed in constant time. The maximum clique algorithm requires only that the overlap model satisfy the Helly property. In both cases, the size of the overlap model must be bounded by a polynomial in the size of the graph. The conditions for both algorithms are satisfied by the class of overlap graphs of subtrees in a tree, which contains chordal graphs, circle graphs, circular-arc graphs, cocomparability graphs, and polygon-circle graphs.