5 papers
A general switching method for constructing E-cospectral hypergraphs
Aida Abiad, Joshua Cooper, Utku Okur
Spectral hypergraph theory studies the structural properties of a hypergraph that can be inferred from the eigenvalues and the eigenvectors of either matrices or tensors associated…
Reconstruction of caterpillar tanglegrams
Ann Clifton, Eva Czabarka, Kevin Liu +4
A tanglegram consists of two rooted binary trees with the same number of leaves and a perfect matching between the leaves of the trees. Given a size- tanglegram, i.e., a tangleg…
Multigraphs with Unique Partition into Cycles
Joshua Cooper, Utku Okur
Due to Veblen's Theorem, if a connected multigraph has even degrees at each vertex, then it is Eulerian and its edge set has a partition into cycles. In this paper, we show tha…
Partitions of an Eulerian Digraph into Circuits
Joshua Cooper, Utku Okur
We investigate a cancellation property satisfied by a connected Eulerian digraph . Namely, unless is a single directed cycle, we have , whe…
Characteristic Polynomials and Hypergraph Generating Functions via Heaps of Pieces
Joshua Cooper, Krystal Guo, Utku Okur
It is a classical result due to Jacobi in algebraic combinatorics that the generating function of closed walks at a vertex in a graph is determined by the rational function…