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18 papers · 1 filter
Total Cut Complexes of Graphs
Margaret Bayer, Mark Denker, Marija Jelić Milutinović +3
Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the \emph{total -cut complex} of a graph to be the simplicial complex whose facets are the complem…
Graphs with Many Hamiltonian Paths
Erik Carlson, Willem Fletcher, MurphyKate Montee +3
A graph is \emph{hamiltonian-connected} if every pair of vertices can be connected by a hamiltonian path, and it is \emph{hamiltonian} if it contains a hamiltonian cycle. We constr…
The Region Smoothing Swap Game
Allison Henrich, Inga Johnson, Jonah Ostroff
We introduce a topological combinatorial game called the Region Smoothing Swap Game. The game is played on a game board derived from the connected shadow of a link diagram on a (po…
Linear algebraic techniques for spanning tree enumeration
Steven Klee, Matthew T. Stamps
Kirchhoff's Matrix-Tree Theorem asserts that the number of spanning trees in a finite graph can be computed from the determinant of any of its reduced Laplacian matrices. In many c…
Linear algebraic techniques for weighted spanning tree enumeration
Steven Klee, Matthew T. Stamps
The weighted spanning tree enumerator of a graph with weighted edges is the sum of the products of edge weights over all the spanning trees in . In the special case that all…
A lower bound theorem for centrally symmetric simplicial polytopes
Steven Klee, Eran Nevo, Isabella Novik +1
Stanley proved that for any centrally symmetric simplicial -polytope with , . We provide a characterization of centrally symmetric -…