Discrepancy and Signed Domination in Graphs and Hypergraphs

Details Discrepancy and Signed Domination in Graphs and Hypergraphs Discrepancy and Signed Domination in Graphs and Hypergraphs

2009-06-22

arxiv.org/abs/0906.3993v1

Mathematics

Combinatorics

12 pages

Scientific paper

For a graph G, a signed domination function of G is a two-colouring of the vertices of G with colours +1 and -1 such that the closed neighbourhood of every vertex contains more +1's than -1's. This concept is closely related to combinatorial discrepancy theory as shown by Fueredi and Mubayi [J. Combin. Theory, Ser. B 76 (1999) 223-239]. The signed domination number of G is the minimum of the sum of colours for all vertices, taken over all signed domination functions of G. In this paper, we present new upper and lower bounds for the signed domination number. These new bounds improve a number of known results.

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