Vector connectivity in graphs

Endre Boros, Pinar Heggernes, Pim Van T'Hof, Martin Milanić

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


Motivated by challenges related to domination, connectivity, and information propagation in social and other networks, we initiate the study of the VECTOR DOMINATIVITY problem. This problem takes as input a graph G and an integer kυ for every vertex υ of G, and the objective is to find a vertex subset S of minimum cardinality such that every vertex ε either belongs to S, or is connected to at least kε vertices of S by disjoint paths. If we require each path to be of length exactly 1, we get the well-known VECTOR DOMINATION problem, which is a generalization of the famous DOMINATION SET problem and several of its variants. Consequently, our problem becomes NP-hard if an upper bound on the length of the disjoint paths is also supplied as input. Due to the hardness of these domination variants even on restricted graph classes, like split graphs, VECTOR DOMINATIVITY seems to be a natural problem to study for drawing the boundaries of tractability for this type of problems. We show that VECTOR DOMINATIVITY can actually be solved in polynomial time on split graphs, in addition to cographs and trees. We also show that the problem can be approximated in polynomial time within a factor of lnn + 2 on all graphs.

Original languageEnglish (US)
Title of host publicationTheory and Applications of Models of Computation - 10th International Conference, TAMC 2013, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783642382352
StatePublished - 2013
Event10th International Conference on Theory and Applications of Models of Computation, TAMC 2013 - Hong Kong, China
Duration: May 20 2013May 22 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7876 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other10th International Conference on Theory and Applications of Models of Computation, TAMC 2013
CityHong Kong

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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