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Algorithms 2015, 8(1), 46-59;

Recognition of Unipolar and Generalised Split Graphs

Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, United Kingdom
Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX 13QD, United Kingdom
Author to whom correspondence should be addressed.
Academic Editor: Abu-Khzam Faisal
Received: 4 July 2014 / Accepted: 26 January 2015 / Published: 13 February 2015
View Full-Text   |   Download PDF [263 KB, uploaded 13 February 2015]


A graph is unipolar if it can be partitioned into a clique and a disjoint union of cliques, and a graph is a generalised split graph if it or its complement is unipolar. A unipolar partition of a graph can be used to find efficiently the clique number, the stability number, the chromatic number, and to solve other problems that are hard for general graphs. We present an O(n2)-time algorithm for recognition of n-vertex generalised split graphs, improving on previous O(n3)-time algorithms. View Full-Text
Keywords: unipolar graphs, generalised split graphs, perfect graphs, recognition algorithms, representations unipolar graphs, generalised split graphs, perfect graphs, recognition algorithms, representations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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McDiarmid, C.; Yolov, N. Recognition of Unipolar and Generalised Split Graphs. Algorithms 2015, 8, 46-59.

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