8 papers · 1 filter
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…
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…
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…
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…
Polynomial Reconstruction Problem for Hypergraphs
Joshua Cooper, Utku Okur
We show that, in general, the characteristic polynomial of a hypergraph is not determined by its ``polynomial deck'', the multiset of characteristic polynomials of its vertex-delet…
Decks of rooted binary trees
Ann Clifton, Eva Czabarka, Audace Dossou-Olory +5
We consider extremal problems related to decks and multidecks of rooted binary trees (a.k.a. rooted phylogenetic tree shapes). Here, the deck (resp. multideck) of a tree refers…
Universal rooted phylogenetic tree shapes and universal tanglegrams
Ann Clifton, Eva Czabarka, Kevin Liu +4
We provide an lower bound and an upper bound for the smallest size of rooted binary trees (a.k.a. phylogenetic tree shapes), which are universal for rooted b…