Signed Domination in Regular Graphs and Set-Systems

Z. Füredi, Dhruv Mubayi

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

Suppose G is a graph on n vertices with minimum degree r. Using standard random methods it is shown that there exists a two-coloring of the vertices of G with colors, +1 and -1, such that all closed neighborhoods contain more 1's than -1's, and all together the number of 1's does not exceed the number of -1's by more than (4logr/r+1/r)n. For large r this greatly improves earlier results and is almost optimal, since starting with an Hadamard matrix of order r, a bipartite r-regular graph is constructed on 4r vertices with signed domination number at least (1/2) r-O(1). The determination of limn→∞γs(G)/n remains open and is conjectured to be Θ(1/r).

Original languageEnglish
Pages (from-to)223-239
Number of pages17
JournalJournal of Combinatorial Theory. Series B
Volume76
Issue number2
DOIs
Publication statusPublished - Jul 1999

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Hadamard matrices
Regular Sets
Set Systems
Coloring
Domination
Signed
Regular Graph
Signed number
Color
Hadamard Matrix
Domination number
Minimum Degree
Colouring
Exceed
Closed
Graph in graph theory
Standards

Keywords

  • Discrepancy
  • Domination
  • Hadamard matrices
  • Random covering of graphs and hypergraphs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Signed Domination in Regular Graphs and Set-Systems. / Füredi, Z.; Mubayi, Dhruv.

In: Journal of Combinatorial Theory. Series B, Vol. 76, No. 2, 07.1999, p. 223-239.

Research output: Contribution to journalArticle

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