Testing k-colorability

Let G be a graph on n vertices and suppose that at least n2 edges have to be deleted from it to make it k-colorable. It is shown that in this case most induced subgraphs of G on ck ln k/ 2 vertices are not k-colorable, where c > 0 is an absolute constant. If G is as above for k = 2, then most induced subgraphs on (ln(1/ ))b are non-bipartite, for some absolute positive constant b, and this is tight up to the poly-logarithmic factor. Both results are motivated by the study of testing algorithms for k-colorability, first considered by Goldreich, Goldwasser and Ron in [3], and improve the results in that paper.

• Type: Journal
• Year: 2002
• Where: SIAMDM
• Authors: Noga Alon, Michael Krivelevich
• Keywords: Absolute Constant, Ck Ln, Paper, SIAMDM 2002