Related papers: Vector-relation configurations and plabic graphs
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
A vertex $v$ of a 2-connected cubic graph $G$ is $\lambda$-matchable if $G$ has a spanning subgraph in which $v$ has degree three whereas every other vertex has degree one, and we let $\lambda(G)$ denote the number of such vertices.…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
This paper introduces new invariants of rigid vertex graph embeddings by using non-local combinatorial information that is available at each graphical node. The new non-local information that we use in this paper involves parity in the…
We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
An input-output model for networks with link uncertainty is developed. The main result presents a set of integral quadratic constraints (IQCs) that collectively imply robust stability of the uncertain network dynamics. The model dependency…
We generalize the construction of the Heegaard Floer homology for a singular knot to that for a balanced bipartite graph. For a given graph, we provide a combinatorial description of the Euler characteristic of its Heegaard Floer homology…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
We define pure graphs, invertible graphs, and the notion of complementation of bicoloured graphs. The study of pure graphs is motivated by two conjectures about the transition systems of eulerian graphs and by the Cycle Double Cover…
Let $V$ be a left vector space over a division ring and let ${\mathcal P}(V)$ be the associated projective space. We describe all finite subsets $X\subset V$ such that every permutation on $X$ can be extended to a linear automorphism of $V$…
There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a…
In this paper, we study two problems related to planar matchings in random bipartite graphs. First, we colour each edge of the complete bipartite graph $K_{n,n}$ uniformly randomly from amongst ${r}$ colours and show that if ${r}$ grows…
Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is well-known. A general…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
In this note we present some abstract ideas how one can construct spaces from building blocks according to a graph. The coupling is expressed via boundary pairs, and can be applied to very different spaces such as discrete graphs, quantum…
Subgraph reconfiguration is a family of problems focusing on the reachability of the solution space in which feasible solutions are subgraphs, represented either as sets of vertices or sets of edges, satisfying a prescribed graph structure…
It is known that the homogeneous coordinate ring of a Grassmannian has a cluster structure, which is induced from the combinatorial structure of a plabic graph. A plabic graph is a certain bipartite graph described on the disk, and there is…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
We study the undirected divisibility graph in which the vertex set is a finite subset of consecutive natural numbers up to N.We derive analytical expressions for measures of the graph like degree, clustering, geodesic distance and…