# Efficient Algorithms for Circular-Arc Containment Graphs

 dc.contributor.advisor Nakajima, K. en_US dc.contributor.author Nirkhe, M.V. en_US dc.date.accessioned 2007-05-23T09:40:35Z dc.date.available 2007-05-23T09:40:35Z dc.date.issued 1987 en_US dc.identifier.uri http://hdl.handle.net/1903/4732 dc.description.abstract In the recent past, a wide variety of algorithms have been developed for a class of intersection graphs, called interval graphs. As a generalization of interval graphs, circular-arc graphs have also been studied extensively. Another category of graphs, namely containment graphs, has recently received some attention. In particular, interval containment graphs have been studied recently and several optimal algorithms have been developed for this class of graphs. In this thesis we introduce a new class of containment graphs called circular-arc containment graphs. A circular-arc containment graph is a generalization of an interval containment graph and is defined as follows: A graph G sub A = (V sub A, E sub A) is called a ciruclar-arc containment graph for a family A = {A sub 1, A sub n} of arcs on a circle, if for each v sub i V sub A, there is an arc A sub i A, and (v sub i, v sub j) E sub A if and only if one of A sub i and A sub j contains the other. We characterize this class of graphs by establishing its equivalence to another relatively new class of intersection graphs, called circular permutation graphs. Given a circular-arc containment graph in the form of a family of arcs on a circle, we develop efficient algorithms for finding a maximum clique, a maximum independent set, and a minimum coloring of the graph. en_US dc.format.extent 1866713 bytes dc.format.mimetype application/pdf dc.language.iso en_US en_US dc.relation.ispartofseries ISR; MS 1987-11 en_US dc.subject Systems Integration en_US dc.title Efficient Algorithms for Circular-Arc Containment Graphs en_US dc.type Thesis en_US dc.contributor.department ISR en_US
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