2023/12/13 by Dubroff, Quentin, Gunby, Benjamin, Narayanan, Bhargav +1 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2312.08265
We study how many copies of a graph F that another graph G with a given number of cliques is guaranteed to have. For example, one of our main results states that for all t≥ 2, if G is an n vertex graph with kn3/2 triangles and k is sufficiently large in terms of t, then G contains at least Ω(min\kt n3/2,k(2t2)/(3t-1)n(5t-2)/(3t-1)\) copies of K2,t, and furthermore, we show these bounds are essentially best-possible provided either k≥ n1/2t or if certain bipartite-analogues of well known conjectures for Turán numbers hold.