6 papers
A Consistent Sandpile Torsor Algorithm for Regular Matroids
Changxin Ding, Alex McDonough, Lilla Tóthmérész +1
Every regular matroid is associated with a sandpile group, which acts simply transitively on the set of bases in various ways. Ganguly and the second author introduced the notion o…
On Canonical Sandpile Actions of Embedded Graphs
Lilla Tóthmérész
The sandpile group of a connected graph is a group whose cardinality is the number of spanning trees. The group is known to have a canonical simply transitive action on spanning tr…
Graph minors, Ehrhart theory, and a monotonicity property
Tamás Kálmán, Lilla Tóthmérész
We study the extended root polytope associated to a directed graph. We show that under the operations of deletion and contraction of an edge of the graph, none of the coefficients…
Degrees of interior polynomials and parking function enumerators
Tamás Kálmán, Lilla Tóthmérész
The interior polynomial of a directed graph is defined as the -polynomial of the graph's (extended) root polytope, and it displays several attractive properties. Here we expre…
Extremal number of arborescences
Aditya Bandekar, Péter Csikvári, Benjamin Mascuch +3
In this paper we study the following extremal graph theoretic problem: Given an undirected Eulerian graph , which Eulerian orientation minimizes or maximizes the number of arbor…
The two-variable hypergraph Tutte polynomial via embedding activities
Lilla Tóthmérész
We prove that the two-variable Tutte polynomial of hypergraphs can be defined via embedding activities. We also prove that embedding activities of hypergraphs yield a Crapo-style d…