Related papers: Coupling Dimers to CDT
A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…
Generalized causal dynamical triangulations (generalized CDT) is a model of two-dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur. We solve the model at the discretized level using…
In this note we revisit the dart graph and the squared dart digraph constructions and prove that they yield strongly connected digraphs when applied to connected graphs of minimum valence at least 3.
We investigate the connections between tree amalgamations and quasi-isometries. In particular, we prove that the quasi-isometry type of multi-ended accessible quasi-transitive connected locally finite graphs is determined by the…
Hypermaps were introduced as an algebraic tool for the representation of embeddings of graphs on an orientable surface. Recently a bijection was given between hypermaps and indecomposable permutations; this sheds new light on the subject by…
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath…
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed…
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
Analyzing large, multivariate graphs is an important problem in many domains, yet such graphs are challenging to visualize. In this paper, we introduce a novel, scalable, tree+table multivariate graph visualization technique, which makes…
We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…
Let $G$ be a $p$-group. We begin to consider the relationship between the structure of the commuting graph and $|G:Z(G)|$. We also build a family of groups whose commuting graphs have more than one connected component whose diameter is at…
We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and…
We have applied the graph theory to estimation of interactions between electronic excitations in molecular crystals. Intramolecular and intermolecular excitations have been considered. The intermolecular interactions contain molecular…
In the theory of line graphs of undirected graphs there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, the exists no analogous…
We construct dimer graphs for type D relativistic Toda models by introducing impurities to the $Y^{2N,0}$ square dimer graphs. By properly placing the impurities and change of canonical variables assigned to the 1-loops on the dimer graph,…
In an earlier work, the author together with Guo [Hermitian adjacency matrix of digraphs and mixed graphs, J. Graph Theory 85 (2017) 217-248] introduced the Hermitian adjacency matrix of directed (and partially directed) graphs. However, it…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
In this paper we provide a principled approach to solve a transductive classification problem involving a similar graph (edges tend to connect nodes with same labels) and a dissimilar graph (edges tend to connect nodes with opposing…