相关论文: Volume inequalities for flow polytopes of full dir…

The analysis of networks, aimed at suitably defined functionality, often focuses on partitions into subnetworks that capture desired features. Chief among the relevant concepts is a 2-partition, that underlies the classical Cheeger…

We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…

A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is…

Adapting Lindstr\"om's well-known construction, we consider a wide class of functions which are generated by flows in a planar acyclic directed graph whose vertices (or edges) take weights in an arbitrary commutative semiring. We give a…

For a weighted directed multigraph, let $f_{ij}$ be the total weight of spanning converging forests that have vertex $i$ in a tree converging to $j$. We prove that $f_{ij} f_{jk} = f_{ik} f_{jj}$ if and only if every directed path from $i$…

In a series of three papers we develop an end space theory for directed graphs. As for undirected graphs, the ends of a digraph are points at infinity to which its rays converge. Unlike for undirected graphs, some ends are joined by limit…

A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…

We introduce the Tesler polytope Tes_n(a_1,a_2,...,a_n), whose integer points are the Tesler matrices of size n with nonnegative integer hook sums a_1,a_2,...,a_n. We show that Tes_n(a) is a flow polytope and therefore the number of Tesler…

We study basic properties of flow equivalence on one-dimensional compact metric spaces with a particular emphasis on isotopy in the group of (self-) flow equivalences on such a space. In particular, we show that an orbit-preserving such map…

The maximum number of vertices in a graph of maximum degree $\Delta\ge 3$ and fixed diameter $k\ge 2$ is upper bounded by $(1+o(1))(\Delta-1)^{k}$. If we restrict our graphs to certain classes, better upper bounds are known. For instance,…

This paper studies signed graphs with possible outer-edges. We introduce and investigate the chain group, the boundary operator, the co-boundary operator, the flow group, the tension group, the homology group, the cohomology group, with…

Network flow interdiction analysis studies by how much the value of a maximum flow in a network can be diminished by removing components of the network constrained to some budget. Although this problem is strongly NP-complete on general…

For an angle $\alpha\in (0,\pi)$, we consider plane graphs and multigraphs in which the edges are either (i) one-bend polylines with an angle $\alpha$ between the two edge segments, or (ii) circular arcs of central angle $2(\pi-\alpha)$. We…

Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…

We show that the Voronoi cells of the lattice of integer flows of a finite connected graph $G$ in the quadratic vector space of real valued flows have the following very precise combinatorics: the face poset of a Voronoi cell is isomorphic…

Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward $k$-planar drawings of…

A graph class is monotone if it is closed under taking subgraphs. It is known that a monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a so-called tripod, that is, a…

The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…

For a bridgeless graph $G$, its flow polynomial is defined to be the function $F(G,q)$ which counts the number of nonwhere-zero $\Gamma$-flows on an orientation of $G$ whenever $q$ is a positive integer and $\Gamma$ is an additive Abelian…

The single-source unsplittable flow (SSUF) problem asks to send flow from a common source to different terminals with unrelated demands, each terminal being served through a single path. One of the most heavily studied SSUF objectives is to…