Abstract
In this paper, we establish structural properties of cographs which enable us to present an algorithm which, for a cograph G and a non-edge xy (i.e., two non-adjacent vertices x and y) of G, finds the minimum number of edges that need to be added to the edge set of G such that the resulting graph is a cograph and contains the edge xy. The motivation for this problem comes from algorithms for the dynamic recognition and online maintenance of graphs; the proposed algorithm could be a suitable addition to the algorithm of Shamir and Sharan [13] for the online maintenance of cographs. The proposed algorithm runs in time linear in the size of the input graph and requires linear space.
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Nikolopoulos, S.D., Palios, L. (2005). Adding an Edge in a Cograph. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_19
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DOI: https://doi.org/10.1007/11604686_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31000-6
Online ISBN: 978-3-540-31468-4
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