We present a common generalization of counting lattice points in rational polytopes and the
enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and …

Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple
graphs. In the present paper we highlight their connections to the Kuramoto synchronization …

Starting from any finite simple graph, one can build a reflexive polytope known as a
symmetric edge polytope. The first goal of this paper is to show that symmetric edge …

For two pairs of vertices x 1, y 1 and x 2, y 2, Seymour and Thomassen independently
presented a characterization of graphs containing no edge-disjoint (x 1, y 1)-path and (x 2, y …

Given an oriented graph G, the modular flow polynomial\phi_G (k) counts the number of
nowhere-zero Z _k-flows of G. We give a description of the modular flow polynomial in terms …

We study quasipolynomials enumerating proper colorings, nowhere-zero tensions, and
nowhere-zero flows in an arbitrary CW-complex X, generalizing the chromatic, tension and …

The Ehrhart polynomial $ L_P $ of an integral polytope $ P $ counts the number of integer
points in integral dilates of $ P $. Ehrhart polynomials of polytopes are often described in …

There is a well-established dictionary between zonotopes, hyperplane arrangements, and
their (oriented) matroids. Arguably one of the most famous examples is the class of graphical …

Nowhere-zero flows in signed graphs: A survey arXiv:1608.06944v1 [math.CO] 24 Aug 2016
Page 1 Nowhere-zero flows in signed graphs: A survey Tomáš Kaiser ∗ Robert Lukot’ka † Edita …

In a bidirected graph, each end of each edge is independently oriented. We show how to
express any column of the incidence matrix as a half‐integral linear combination of any …