Vertex cover gets faster and harder on low degree graphs

Akanksha Agrawal, Sathish Govindarajan, Neeldhara Misra

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


The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637 k n O(1).

Original languageEnglish
Title of host publicationComputing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319087825
StatePublished - 1 Jan 2014
Externally publishedYes
Event20th International Computing and Combinatorics Conference, COCOON 2014 - Atlanta, GA, United States
Duration: 4 Aug 20146 Aug 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8591 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th International Computing and Combinatorics Conference, COCOON 2014
Country/TerritoryUnited States
CityAtlanta, GA

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


Dive into the research topics of 'Vertex cover gets faster and harder on low degree graphs'. Together they form a unique fingerprint.

Cite this