4 papers · 1 filter
Many cliques with few edges
Rachel Kirsch, A. J. Radcliffe
Recently Cutler and Radcliffe proved that the graph on vertices with maximum degree at most having the most cliques is a disjoint union of cliques…
Maximizing 2-Independent Sets in 3-Uniform Hypergraphs
Lauren Keough, A. J. Radcliffe
There has been interest recently in maximizing the number of independent sets in graphs. For example, the Kahn-Zhao theorem gives an upper bound on the number of independent sets i…
Extremal Threshold Graphs for Matchings and Independent Sets
L. Keough, A. J. Radcliffe
Many extremal problems for graphs have threshold graphs as their extremal examples. For instance the current authors proved that for fixed , among all graphs on vertice…
Counting dominating sets and related structures in graphs
Jonathan Cutler, A. J. Radcliffe
We consider some problems concerning the maximum number of (strong) dominating sets in a regular graph, and their weighted analogues. Our primary tool is Shearer's entropy lemma. T…