A note on chromatic properties of threshold graphs

Ries, Bernard; de Werra, Dominique; Zenklusen, Rico

doi:10.1016/j.disc.2012.01.036

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Journal article

A note on chromatic properties of threshold graphs

Ries, Bernard University of Fribourg, Switzerland
de Werra, Dominique EPFL, Switzerland
Zenklusen, Rico Massachusetts Institute of Technology, USA

2012

Published in:

Discrete Mathematics. - 2012, vol. 312, no. 10, p. 1838-1843

Theoretical Computer Science

Discrete Mathematics and Combinatorics

English In threshold graphs one may find weights for the vertices and a threshold value t such that for any subset S of vertices, the sum of the weights is at most the threshold t if and only if the set S is a stable (independent) set. In this note we ask a similar question about vertex colorings: given an integer p, when is it possible to find weights (in general depending on p) for the vertices and a threshold value tp such that for any subset S of vertices the sum of the weights is at most tp if and only if S generates a subgraph with chromatic number at most p − 1? We show that threshold graphs do have this property and we show that one can even find weights which are valid for all values of p simultaneously.

Faculty

Faculté des sciences économiques et sociales et du management

Department

Département d'informatique

Language