TY - JOUR
T1 - Sizes of induced subgraphs of Ramsey graphs
AU - Alon, Noga
AU - Balogh, József
AU - Kostochka, Alexandr
AU - Samotij, Wojciech
PY - 2009/7
Y1 - 2009/7
N2 - An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdo″s, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n5/2) induced subgraphs, any two of which differ either in the number of vertices or in the number of edges, i.e., the number of distinct pairs (|V(H)|, |E(H)|), as H ranges over all induced subgraphs of G, is Ω(n5/2). We prove an Ω(n2.3693) lower bound.
AB - An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdo″s, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n5/2) induced subgraphs, any two of which differ either in the number of vertices or in the number of edges, i.e., the number of distinct pairs (|V(H)|, |E(H)|), as H ranges over all induced subgraphs of G, is Ω(n5/2). We prove an Ω(n2.3693) lower bound.
UR - http://www.scopus.com/inward/record.url?scp=70149117945&partnerID=8YFLogxK
U2 - 10.1017/S0963548309009869
DO - 10.1017/S0963548309009869
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AN - SCOPUS:70149117945
VL - 18
SP - 459
EP - 476
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
SN - 0963-5483
IS - 4
ER -