ON THE NUMBER OF CERTAIN SUBGRAPHS CONTAINED IN GRAPHS WITH A GIVEN NUMBER OF EDGES BY NOGA ALON School of Mathematical Sciences

@inproceedings{Alon2007ONTN,
title={ON THE NUMBER OF CERTAIN SUBGRAPHS CONTAINED IN GRAPHS WITH A GIVEN NUMBER OF EDGES BY NOGA ALON School of Mathematical Sciences},
author={Noga Alon},
year={2007}
}

All graphs considered are finite, undirected, with no loops, no multiple edges and no isolated vertices. For two graphs G, H, let N(G, H) denote the number of subgraphs of G isomorphic to H. Define also, for l >=0, N(I,H)= max N(G, H), where the maximum is taken over all graphs G with l edges. We determine N(l, H) precisely for all l -> 0 when H is a disjoint union of two stars, and also when H is a disjoint union of r > 3 stars, each of size s or s + 1, where s ->_ r. We also determine N(l, H… CONTINUE READING