Network Majority on Tree Topological Network

Ravindra B. Bapat, Shinya Fujita, Sylvain Legay, Yannis Manoussakis, Yasuko Matsui, Tadashi Sakuma, Z. Tuza

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let G=(V,E) be a graph, and w:V→Q>0 be a positive weight function on the vertices of G. For every subset X of V, let w(X)=∑v∈Gw(v). A non-empty subset S⊂V(G) is a weighted safe set if, for every component C of the subgraph induced by S and every component D of G\S, we have w(C)≥w(D) whenever there is an edge between C and D. In this paper we show that the problem of computing the minimum weight of a safe set is NP-hard for trees, even if the underlining tree is restricted to be a star, but it is polynomially solvable for paths. Then we define the concept of a parameterized infinite family of “proper central subgraphs” on trees, whose polar ends are the minimum-weight connected safe sets and the centroids. We show that each of these central subgraphs includes a centroid. We also give a linear-time algorithm to find all of these subgraphs on unweighted trees.

Original languageEnglish
Pages (from-to)79-84
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume54
DOIs
Publication statusPublished - Oct 1 2016

Fingerprint

Set theory
Stars
Subgraph
Centroid
Connected Set
Subset
Induced Subgraph
Linear-time Algorithm
Weight Function
Star
NP-complete problem
Path
Computing
Graph in graph theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Bapat, R. B., Fujita, S., Legay, S., Manoussakis, Y., Matsui, Y., Sakuma, T., & Tuza, Z. (2016). Network Majority on Tree Topological Network. Electronic Notes in Discrete Mathematics, 54, 79-84. https://doi.org/10.1016/j.endm.2016.09.015

Network Majority on Tree Topological Network. / Bapat, Ravindra B.; Fujita, Shinya; Legay, Sylvain; Manoussakis, Yannis; Matsui, Yasuko; Sakuma, Tadashi; Tuza, Z.

In: Electronic Notes in Discrete Mathematics, Vol. 54, 01.10.2016, p. 79-84.

Research output: Contribution to journalArticle

Bapat, RB, Fujita, S, Legay, S, Manoussakis, Y, Matsui, Y, Sakuma, T & Tuza, Z 2016, 'Network Majority on Tree Topological Network', Electronic Notes in Discrete Mathematics, vol. 54, pp. 79-84. https://doi.org/10.1016/j.endm.2016.09.015
Bapat RB, Fujita S, Legay S, Manoussakis Y, Matsui Y, Sakuma T et al. Network Majority on Tree Topological Network. Electronic Notes in Discrete Mathematics. 2016 Oct 1;54:79-84. https://doi.org/10.1016/j.endm.2016.09.015
Bapat, Ravindra B. ; Fujita, Shinya ; Legay, Sylvain ; Manoussakis, Yannis ; Matsui, Yasuko ; Sakuma, Tadashi ; Tuza, Z. / Network Majority on Tree Topological Network. In: Electronic Notes in Discrete Mathematics. 2016 ; Vol. 54. pp. 79-84.
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