Densities of 3-vertex graphs
Combinatorics
2017-04-12 v3
Abstract
Let d_i(G) be the density of the 3-vertex i-edge graph in a graph G, i.e., the probability that three random vertices induce a subgraph with i edges. Let S be the set of all quadruples (d_0,d_1,d_2,d_3) that are arbitrary close to 3-vertex graph densities in arbitrary large graphs. Huang, Linial, Naves, Peled and Sudakov have recently determined the projection of the set S to the (d_0,d_3) plane. We determine the projection of the set S to all the remaining planes.
Cite
@article{arxiv.1610.02446,
title = {Densities of 3-vertex graphs},
author = {Roman Glebov and Andrzej Grzesik and Ping Hu and Tamas Hubai and Daniel Kral and Jan Volec},
journal= {arXiv preprint arXiv:1610.02446},
year = {2017}
}
Comments
We have recently noticed a miscalculation in the proof of Lemma 7 and are preparing a revision of the manuscript