On the Signed Domination in Graphs

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.

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Additional information

Received May 12, 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Matoušek, J. On the Signed Domination in Graphs. Combinatorica 20, 103–108 (2000). https://doi.org/10.1007/s004930070034

Download citation

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