A Polynomial Kernel for Proper Interval Vertex Deletion

Fomin, Fedor V. ; Saurabh, Saket ; Villanger, Yngve (2013) A Polynomial Kernel for Proper Interval Vertex Deletion SIAM Journal on Discrete Mathematics, 27 (4). pp. 1964-1976. ISSN 0895-4801

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Official URL: http://doi.org/10.1137/12089051X

Related URL: http://dx.doi.org/10.1137/12089051X

Abstract

It is known that the problem of deleting at most $k$ vertices to obtain a proper interval graph (Proper Interval Vertex Deletion) is fixed parameter tractable. However, whether the problem admits a polynomial kernel or not was open. Here, we answer this question in the affirmative by obtaining a polynomial kernel for Proper Interval Vertex Deletion. This resolves an open question of van Bevern et al.

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