Abstract
In this paper we give a necessary condition and a sufficient condition for a graph to be a pairwise compatibility graph (PCG). Let G be a graph and let \(G^c\) be the complement of G. We show that if \(G^c\) has two disjoint chordless cycles then G is not a PCG. On the other hand, if \(G^c\) has no cycle then G is a PCG. Our conditions are the first necessary condition and the first sufficient condition for pairwise compatibility graphs in general.
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Acknowledgment
This work is done in the Department of Computer Science and Engineering (CSE) of Bangladesh University of Engineering and Technology (BUET). The authors gratefully acknowledge the support received from BUET.
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Hossain, M.I., Salma, S.A., Rahman, M.S. (2016). A Necessary Condition and a Sufficient Condition for Pairwise Compatibility Graphs. In: Kaykobad, M., Petreschi, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2016. Lecture Notes in Computer Science(), vol 9627. Springer, Cham. https://doi.org/10.1007/978-3-319-30139-6_9
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DOI: https://doi.org/10.1007/978-3-319-30139-6_9
Publisher Name: Springer, Cham
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