3 citations · 8 across the 6 of their papers we have counts for
6 papers · 1 filter
4-Chromatic Graphs Have At Least 4 Cycles of Length
Sean Kim, Michael E. Picollelli
A 2018 conjecture of Brewster, McGuinness, Moore, and Noel asserts that for , if a graph has chromatic number greater than , then it contains at least as many cycles of…
The independent neighborhoods process
Tom Bohman, Dhruv Mubayi, Michael Picollelli
A triangle in an -uniform hypergraph is a set of edges such that of them share a common -set of vertices and the last edge contains the remaining vert…
Complete r-partite graphs determined by their domination polynomial
Barbara M. Anthony, Michael E. Picollelli
The domination polynomial of a graph is the polynomial whose coefficients count the number of dominating sets of each cardinality. A recent question asks which graphs are uniquely…
The final size of the C_4-free process
Michael E. Picollelli
We consider the following random graph process: starting with n isolated vertices, add edges uniformly at random provided no such edge creates a copy of C_4. We show that, with pro…
The diamond-free process
Michael E. Picollelli
Let K_4^- denote the diamond graph, formed by removing an edge from the complete graph K_4. We consider the following random graph process: starting with n isolated vertices, add e…
Set systems without a 3-simplex
Michael E. Picollelli
A 3-simplex is a collection of four sets A_1,...,A_4 with empty intersection such that any three of them have nonempty intersection. We show that the maximum size of a set system o…