TY - JOUR

T1 - Testing k-colorability

AU - Alon, Noga

AU - Krivelevich, Michael

PY - 2002/2

Y1 - 2002/2

N2 - Let G be a graph on n vertices and suppose that at least εn2 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/ε2 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/ε))b/ε are nonbipartite, for some absolute positive constant b, and this is tight up to the polylogarithmic factor. Both results are motivated by the study of testing algorithms for k-colorability, first considered by Goldreich, Goldwasser, and Ron in [J. ACM, 45 (1998), pp. 653-750], and improve the results in that paper.

AB - Let G be a graph on n vertices and suppose that at least εn2 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/ε2 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/ε))b/ε are nonbipartite, for some absolute positive constant b, and this is tight up to the polylogarithmic factor. Both results are motivated by the study of testing algorithms for k-colorability, first considered by Goldreich, Goldwasser, and Ron in [J. ACM, 45 (1998), pp. 653-750], and improve the results in that paper.

KW - Graph coloring

KW - Property testing

UR - http://www.scopus.com/inward/record.url?scp=0036487485&partnerID=8YFLogxK

U2 - 10.1137/S0895480199358655

DO - 10.1137/S0895480199358655

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AN - SCOPUS:0036487485

SN - 0895-4801

VL - 15

SP - 211

EP - 227

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 2

ER -