7 citations · 17 across the 8 of their papers we have counts for
10 papers
On approximating the rank of graph divisors
Kristóf Bérczi, Hung P. Hoang, Lilla Tóthmérész
Baker and Norine initiated the study of graph divisors as a graph-theoretic analogue of the Riemann-Roch theory for Riemann surfaces. One of the key concepts of graph divisor theor…
A geometric proof for the root-independence of the greedoid polynomial of Eulerian branching greedoids
Lilla Tóthmérész
We define the root polytope of a regular oriented matroid, and show that the greedoid polynomial of an Eulerian branching greedoid rooted at vertex is equivalent to the …
Ehrhart theory of symmetric edge polytopes via ribbon structures
Tamás Kálmán, Lilla Tóthmérész
Using a ribbon structure of the graph, we construct a dissection of the symmetric edge polytope of a graph into unimodular simplices. Our dissection is shellable, and one can inter…
Root polytopes and Jaeger-type dissections for directed graphs
Tamás Kálmán, Lilla Tóthmérész
We associate root polytopes to directed graphs and study them by using ribbon structures. Most attention is paid to what we call the semi-balanced case, i.e., when each cycle has t…
Rotor-routing reachability is easy, chip-firing reachability is hard
Lilla Tóthmérész
Chip-firing and rotor-routing are two well-studied examples of abelian networks. We study the complexity of their respective reachability problems. We show that the rotor-routing r…
The devil's staircase for chip-firing on random graphs and on graphons
Viktor Kiss, Lionel Levine, Lilla Tóthmérész
We study the behavior of the activity of the parallel chip-firing upon increasing the number of chips on an Erdős--Rényi random graph. We show that in various situations the result…
The sandpile group of a trinity and a canonical definition for the planar Bernardi action
Tamás Kálmán, Seunghun Lee, Lilla Tóthmérész
Baker and Wang define the so-called Bernardi action of the sandpile group of a ribbon graph on the set of its spanning trees. This potentially depends on a fixed vertex of the grap…
Hypergraph polynomials and the Bernardi process
Tamás Kálmán, Lilla Tóthmérész
Recently O. Bernardi gave a formula for the Tutte polynomial of a graph, based on spanning trees and activities just like the original definition, but using a fixed ribbon…
Effective divisor classes on metric graphs
Andreas Gross, Farbod Shokrieh, Lilla Tóthmérész
We introduce the notion of semibreak divisors on metric graphs (tropical curves) and prove that every effective divisor class (of degree at most the genus) has a semibreak divisor…
On the complexity of the chip-firing reachability problem
Bálint Hujter, Viktor Kiss, Lilla Tóthmérész
In this paper, we study the complexity of the chip-firing reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in strongly polynomial t…