Quick but Odd Growth of Cacti

Sudeshna Kolay, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Let F be a family of graphs. Given an n-vertex input graph G and a positive integer k, testing whether G has a vertex subset S of size at most k, such that G- S belongs to F, is a prototype vertex deletion problem. These type of problems have attracted a lot of attention in recent times in the domain of parameterized complexity. In this paper, we study two such problems; when F is either the family of forests of cacti or the family of forests of odd-cacti. A graph H is called a forest of cacti if every pair of cycles in H intersect on at most one vertex. Furthermore, a forest of cacti H is called a forest of odd cacti, if every cycle of H is of odd length. Let us denote by C and Codd, the families of forests of cacti and forests of odd cacti, respectively. The vertex deletion problems corresponding to C and Codd are called Diamond Hitting Set and Even Cycle Transversal, respectively. In this paper we design randomized algorithms with worst case run time 12 knO ( 1 ) for both these problems. Our algorithms considerably improve the running time for Diamond Hitting Set and Even Cycle Transversal, compared to what is known about them.

Original languageEnglish
Pages (from-to)271-290
Number of pages20
Issue number1
StatePublished - 1 Sep 2017
Externally publishedYes


  • Diamond Hitting Set
  • Even Cycle Transversal
  • Fixed parameter tractability
  • Randomized algorithms

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics


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