2021/01/08 by Falgas-Ravry, Victor
#05C22 #05C30 #05C35 #05D99 #Combinatorics (math.CO) #FOS: Mathematics #G.2.1 #G.2.2
paper · doi:10.48550/arxiv.2101.03056
A multigraph G is an (s,q)-graph if every s-set of vertices in G supports at most q edges of G, counting multiplicities. Mubayi and Terry posed the problem of determining the maximum of the product of the edge-multiplicities in an (s,q)-graph on n vertices. We give an asymptotic solution to this problem for the family (s,q)=(2r, a\binom2r2+ex(2r, Kr+1)-1 ) with r, a∈ ℤ≥ 2. This greatly generalises previous results on the problem due to Mubayi and Terry and to Day, Treglown and the author, who between them had resolved the special case r=2. Our result asymptotically confirms an infinite family of cases in (and overcomes a major obstacle to a resolution of) a conjecture of Day, Treglown and the author.