3 citations · 6 across the 8 of their papers we have counts for
9 papers
Distinguishing partitions of complete multipartite graphs
Michael Goff
A \textit{distinguishing partition} of a group with automorphism group is a partition of that is fixed by no nontrivial element of . In the event that…
Edge growth in graph squares
Michael Goff
We resolve a conjecture of Hegarty regarding the number of edges in the square of a regular graph. If is a connected -regular graph with vertices, the graph square of $G…
Extremal Betti numbers of Rips complexes
Michael Goff
Upper bounds on the topological Betti numbers of Vietoris-Rips complexes are established, and examples of such complexes with high Betti numbers are given.
Balanced complexes and complexes without large missing faces
Michael Goff, Steven Klee, Isabella Novik
The face numbers of simplicial complexes without missing faces of dimension larger than are studied. It is shown that among all such -dimensional complexes with non-vani…
Higher dimensional Moore bounds
Michael Goff
We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes t…
Optimal Betti numbers of forest ideals
Michael Goff
We prove a tight lower bound on the Betti numbers of tree and forest ideals and a tight upper bound on certain graded Betti numbers of squarefree monomial ideals.