A faster FPT algorithm and a smaller kernel for block graph vertex deletion

Akanksha Agrawal, Sudeshna Kolay, Daniel Lokshtanov, Saket Saurabh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

22 Scopus citations


A graph G is called a block graph if every maximal 2-connected component of G is a clique. In this paper we study the Block Graph Vertex Deletion from the perspective of fixed parameter tractable (FPT) and kernelization algorithms. In particular, an input to Block Graph Vertex Deletion consists of a graph G and a positive integer k, and the objective to check whether there exists a subset S ⊆ V (G) of size at most k such that the graph induced on V (G)\S is a block graph. In this paper we give an FPT algorithm with running time 4knO(1) and a polynomial kernel of size O(k4) for Block Graph Vertex Deletion. The running time of our FPT algorithm improves over the previous best algorithm for the problem that runs in time 10knO(1), and the size of our kernel reduces over the previously known kernel of size O(k6). Our results are based on a novel connection between Block Graph Vertex Deletion and the classical Feedback Vertex Set problem in graphs without induced C4 and K4 − e. To achieve our results we also obtain an algorithm for Weighted Feedback Vertex Set running in time 3.618knO(1) and improving over the running time of previously known algorithm with running time 5knO(1).

Original languageEnglish
Title of host publicationLATIN 2016
Subtitle of host publicationTheoretical Informatics - 12th Latin American Symposium, Proceedings
EditorsGonzalo Navarro, Evangelos Kranakis, Edgar Chávez
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783662495285
StatePublished - 1 Jan 2016
Externally publishedYes
Event12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico
Duration: 11 Apr 201615 Apr 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th Latin American Symposium on Theoretical Informatics, LATIN 2016

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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