Unit Interval Vertex Deletion: Fewer Vertices are Relevant

Abstract

The unit interval vertex deletion problem asks for a set of at most $k$ vertices whose deletion from an $n$-vertex graph makes it a unit interval graph. We develop an $O(k^4)$-vertex kernel for the problem, significantly improving the $O(k^{53})$-vertex kernel of Fomin, Saurabh, and Villanger [ESA'12; SIAM J. Discrete Math 27(2013)]. We introduce a novel way of organizing cliques of a unit interval graph. Our constructive proof for the correctness of our algorithm, using interval models, greatly simplifies the destructive proofs, based on forbidden induced subgraphs, for similar problems in literature.

References in corpus (2)

• Linear Recognition of Almost Interval Graphs
• A Polynomial Kernel for Trivially Perfect Editing