Ries, Bernard de Werra, Dominique Zenklusen, Rico 2012 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. application/pdf https://folia.unifr.ch/global/documents/307823 https://folia.unifr.ch/documents/307823/files/threshold.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2012.01.036 info:eu-repo/semantics/openAccess License undefined Discrete Mathematics. - 2012, vol. 312, no. 10, p. 1838-1843 Theoretical Computer Science Discrete Mathematics and Combinatorics info:eu-repo/classification/udc/004 A note on chromatic properties of threshold graphs http://purl.org/coar/resource_type/c_6501