Related papers: Manhattan and Chebyshev flows
In fluid mechanics, dimensionless numbers like the Reynolds number help classify flows. We argue that such a classification is also relevant for crowd flows by putting forward the dimensionless Intrusion and Avoidance numbers.Using an…
The paper characterizes $(2t+1)$-regular graphs with circular flow number $2 + \frac{2}{2t-1}$. For $t=1$ this is Tutte's characterization of cubic graphs with flow number 4. The class of cubic graphs is the only class of odd regular graphs…
We introduce and study a multivariate function that counts nowhere-zero flows on a graph G, in which each edge of G has an individual capacity. We prove that the associated counting function is a piecewise-defined polynomial in these…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include regularity results for Manhattan curves, the uniqueness of…
I humbly introduce a concept I call "Fregean flows," a graph theoretic representation of classical logic, to show how higher-dimensional graph characteristics might be useful to prove or perhaps at best show the provability of simple…
Kontsevich's graph flows are -- universally for all finite-dimensional affine Poisson manifolds -- infinitesimal symmetries of the spaces of Poisson brackets. We show that the previously known tetrahedral flow and the recently obtained…
Given a graph $G$, the number of nowhere-zero $\ZZ_q$-flows $\phi_G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero $\ZZ_q$-flows to simplicial complexes $\Delta$ of dimension greater than one, and prove the…
The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform…
Let $H$ and $G$ be graphs. An $H$-colouring of $G$ is a proper edge-colouring $f:E(G)\rightarrow E(H)$ such that for any vertex $u\in V(G)$ there exists a vertex $v\in V(H)$ with $f\left (\partial_Gu\right )=\partial_Hv$, where…
Let $G$ be a connected bridgeless $(n,m)$-graph which may have loops and multiedges, and let $F(G,t)$ denote the flow polynomial of $G$. Dong and Koh \cite{Dong1} established an upper bound for the absolute value of coefficient $c_{i}$ of…
In this paper the concept of circular $r$-flows in a mono-directed signed graph $(G, \sigma)$ is introduced. That is a pair $(D, f)$, where $D$ is an orientation on $G$ and $f: E(G)\to (-r,r)$ satisfies that $|f(e)|\in [1, r-1]$ for each…
Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat $3$-manifolds which we call translation prisms. Using ideas of Furstenberg and Veech, we connect results about weak mixing properties of…
A normal $k$-edge-coloring of a cubic graph is an edge-coloring with $k$ colors having the additional property that when looking at the set of colors assigned to any edge $e$ and the four edges adjacent it, we have either exactly five…
A conjecture of Berge and Fulkerson (1971) states that every cubic bridgeless graph contains 6 perfect matchings covering each edge precisely twice, which easily implies that every cubic bridgeless graph has three perfect matchings with…
An elliptic Newton flow is a dynamical system that can be interpreted as a continuous version of Newton's iteration method for finding the zeros of an elliptic function f. Previous work focusses on structurally stable flows (i.e., the phase…
A signed graph is a graph with a positive or negative sign on each edge. Regarding each edge as two half edges, an orientation of a signed graph is an assignment of a direction to each of its half edges such that the two half edges of a…
A problem by Diestel is to extend algebraic flow theory of finite graphs to infinite graphs with ends. In order to pursue this problem, we define an A-flow and non-elusive H-flow for arbitrary graphs and for abelian topological Hausdorff…
We show that if M is a hyperbolic 3-manifold which admits a quasigeodesic flow, then pi_1(M) acts faithfully on a universal circle by homeomorphisms, and preserves a pair of invariant laminations of this circle. As a corollary, we show that…
Given two graphs $H_1$ and $H_2$, a graph $G$ is $(H_1,H_2)$-free if it contains no subgraph isomorphic to $H_1$ or $H_2$. Let $P_t$ and $C_s$ be the path on $t$ vertices and the cycle on $s$ vertices, respectively. In this paper we show…