Combinatorica

, Volume 20, Issue 1, pp 103–108 | Cite as

On the Signed Domination in Graphs

  • Jiří Matoušek
Original Paper

G

on n vertices with minimum degree r, there exists a two-coloring of the vertices of G with colors +1 and -1, such that the closed neighborhood of each vertex contains more +1's than -1's, and altogether the number of 1's does not exceed the number of -1's by more than \(\). As a construction by Füredi and Mubayi shows, this is asymptotically tight. The proof uses the partial coloring method from combinatorial discrepancy theory.

AMS Subject Classification (1991) Classes:  05C78, 05D15 

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Copyright information

© János Bolyai Mathematical Society, 2000

Authors and Affiliations

  • Jiří Matoušek
    • 1
  1. 1.Department of Applied Mathematics, Charles University; 118 00 Praha 1, Czech Republic; E-mail: matousek@kam.mff.cuni.czCZ

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