TY - JOUR
T1 - Subgraphs with a Large Cochromatic Number
AU - Alon, Noga
AU - Krivelevich, Michael
AU - Sudakov, Benny
PY - 1997/8
Y1 - 1997/8
N2 - The cochromatic number of a graph G = (V, E) is the smallest number of parts in a partition of V in which each part is either an independent set or induces a complete subgraph. We show that if the chromatic number of G is n, then G contains a subgraph with cochromatic number at least Ω(n/lnn). This is tight, up to the constant factor, and settles a problem of Erdos and Gimbel.
AB - The cochromatic number of a graph G = (V, E) is the smallest number of parts in a partition of V in which each part is either an independent set or induces a complete subgraph. We show that if the chromatic number of G is n, then G contains a subgraph with cochromatic number at least Ω(n/lnn). This is tight, up to the constant factor, and settles a problem of Erdos and Gimbel.
KW - Chromatic number
KW - Graph coloring
KW - Ramsey theory
UR - http://www.scopus.com/inward/record.url?scp=0031475889&partnerID=8YFLogxK
U2 - 10.1002/(SICI)1097-0118(199708)25:4<295::AID-JGT7>3.0.CO;2-F
DO - 10.1002/(SICI)1097-0118(199708)25:4<295::AID-JGT7>3.0.CO;2-F
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AN - SCOPUS:0031475889
SN - 0364-9024
VL - 25
SP - 295
EP - 297
JO - Journal of Graph Theory
JF - Journal of Graph Theory
IS - 4
ER -