Related papers: Two-dimensional partial cubes

Parabolic almost conformally symplectic structures were introduced in the first part of this series of articles as a class of geometric structures which have an underlying almost conformally symplectic structure. If this underlying…

An explicit construction of a family of binary LDPC codes called LU(3,q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The…

We introduce shortcut graphs and groups. Shortcut graphs are graphs in which cycles cannot embed without metric distortion. Shortcut groups are groups which act properly and cocompactly on shortcut graphs. These notions unify a surprisingly…

We explore the combination theorem for a group G splitting as a graph of relatively hyperbolic groups. Using the fine graph approach to relative hyperbolicity, we find short proofs of the relative hyperbolicity of G under certain…

A vertical 2-sum of a two-coatom lattice $L$ and a two-atom lattice $U$ is obtained by removing the top of $L$ and the bottom of $U$, and identifying the coatoms of $L$ with the atoms of $U$. This operation creates one or two nonisomorphic…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level…

We construct a combinatorial moduli space closely related to the KSV-compactification of the moduli space of bordered marked Riemann surfaces. The open part arises from symmetric metric ribbon graphs. The compactification is obtained by…

A recent result of one of the authors says that every connected subcubic bipartite graph that is not isomorphic to the Heawood graph has at least one, and in fact a positive proportion of its eigenvalues in the interval [-1,1]. We construct…

In this article we prove new results about the existence of 2-cells in disc diagrams which are extreme in the sense that they are attached to the rest of the diagram along a small connected portion of their boundary cycle. In particular, we…

We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…

Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…

In [8], Arveson proved that a $1$-parameter decomposable product system is isomorphic to the product system of a CCR flow. We show that the structure of a generic decomposable product system, over higher dimensional cones, modulo twists by…

It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…

Quasi-median graphs are a tool commonly used by evolutionary biologists to visualise the evolution of molecular sequences. As with any graph, a quasi-median graph can contain cut vertices, that is, vertices whose removal disconnect the…

A $k$-weak bisection of a cubic graph $G$ is a partition of the vertex-set of $G$ into two parts $V_1$ and $V_2$ of equal size, such that each connected component of the subgraph of $G$ induced by $V_i$ ($i=1,2$) is a tree of at most $k-2$…

Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic. Some of the aspects of this is known to be related to the…

On the basis of recent results on hamiltonicity and hamiltonian connectedness in the square of a 2-block, we determine the most general block-cutvertex structure a graph $G$ may have in order to guarantee that $G^2$ is hamiltonian,…

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied…