Related papers: Nowhere-zero flows in signed graphs: A survey
We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix…
We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…
We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…
Zero forcing parameters, associated with graphs, have been studied for over a decade, and have gained popularity as the number of related applications grows. In particular, it is well-known that such parameters are related to certain vertex…
Tutte's famous 5-flow conjecture asserts that every bridgeless graph has a nowhere-zero 5-flow. Seymour proved that every such graph has a nowhere-zero 6-flow. Here we give (two versions of) a new proof of Seymour's Theorem. Both are…
Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric…
This article is the complement to [quant-ph/0611284], which proves that flows (as introduced by [quant-ph/0506062]) can be found efficiently for patterns in the one-way measurement model which have non-empty input and output subsystems of…
We give a full characterisation of the symmetries of unlabelled triangulations and derive a constructive decomposition of unlabelled triangulations depending on their symmetries. As an application of these results we can deduce a complete…
In this article, various results will be demonstrated that enable the delimitation of a zero-free region for holomorphic functions on a set $K$, studying the behavior of their imaginary or real part on the boundary of $K$. These findings…
We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to 1 or -1. Here we deal with the disconnected, the bipartite and the complete signed graphs.…
Brief development of the idea of the very important notion of continuity is given. Continuity is often confused with contiguity, "drawing the graph in one go," "no gaps," etc. The author argues in support of using correct notions of…
The applications of graph coloring are diverse and many so lots of new types of coloring are being proposed and explored. Here we define a safe k-coloring, motivated by the application of coloring to secret sharing. Secret sharing is a way…
A squarefree word is a sequence $w$ of symbols such that there are no strings $x, y$, and $z$ for which $w=xyyz$. A nonrepetitive coloring of a graph is an edge coloring in which the sequence of colors along any open path is squarefree. We…
We prove new lower bounds on the crossing number of a complete graphs assuming that it is drawn in such a way that it contains a Hamiltonian cycle with no crossings.
We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a…
An important property of chordal graphs is that these graphs are characterized by existence of perfect elimination orderings on their vertex sets. In this paper, we generalize the notion of perfect elimination orderings to signed graphs,…
We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of…
It is well known that a graph $G$ has a symmetric spectrum if and only if it is bipartite, a signed graph $\Gamma=(G,\sigma)$ has a symmetric spectrum if $G$ is bipartite. However, there exists a spectrally symmetric signed graph…
A signed graph is a graph in which each edge has a positive or negative sign. In this article, first we characterize the distance compatibility in the case of a connected signed graph and discussed the distance compatibility criterion for…
The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent…