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Efficient algorithms for interval graphs and circular‐arc graphs
Author(s) -
Gupta U. I.,
Lee D. T.,
Leung J. Y.T.
Publication year - 1982
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230120410
Subject(s) - combinatorics , disjoint sets , mathematics , split graph , interval graph , maximal independent set , interval (graph theory) , cograph , chordal graph , clique , discrete mathematics , independent set , arc (geometry) , indifference graph , clique sum , graph , 1 planar graph , geometry
We show that for an interval graph given in the form of a family of intervals, a maximum independent set, a minimum covering by disjoint completely connected sets or cliques, and a maximum clique can all be found in O ( n log n ) time [ O ( n ) time if the endpoints of the intervals are sorted]. For the more general circular‐arc graphs, a maximum independent set and a minimum covering by disjoint completely connected sets or cliques can be found in O ( n 2 ) time, provided again that a corresponding family of arcs is given.