Related papers: Vertex Collapsing and Cut Ideals

We introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors on edges incident to it. In this paper we investigate the…

Let X* be a subset of an affine space A^s, over a finite field K, which is parameterized by the edges of a clutter. Let X and Y be the images of X* under the maps x --> [x] and x --> [(x,1)] respectively, where [x] and [(x,1)] are points in…

Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…

A matching cut in a graph G is an edge cut of G that is also a matching. This short survey gives an overview of old and new results and open problems for Maximum Matching Cut, which is to determine the size of a largest matching cut in a…

Target class classification is a mixed classification and transition model whose integrated goal is to assign objects to a certain, so called target or normal class. The classification process is iterative, and in each step an object in a…

In this paper we discuss an operation on halving edges graph that we call fission. Fission replaces each point in a given configuration with a small cluster of k points. The operation interacts nicely with halving edges, so we examine its…

Consider a random hypergraph on a set of N vertices in which, for k between 1 and N, a Poisson(N beta_k) number of hyperedges is scattered randomly over all subsets of size k. We collapse the hypergraph by running the following algorithm to…

In this note, we study two rewrite rules on hypergraphs, called edge-domination and node-domination, and show that they are confluent. These rules are rather natural and commonly used before computing the minimum hitting sets of a…

Graph modification problems are typically asked as follows: is there a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and…

In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…

Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…

In this paper, we explain the regularity, projective dimension and depth of edge ideal of some classes of graphs in terms of invariants of graphs. We show that for a $C_5$-free vertex decomposable graph $G$, $\T{reg}(R/I(G))= c_G$, where…

Adjacency polytopes, a.k.a. symmetric edge polytopes, associated with undirected graphs have been defined and studied in several seemingly independent areas including number theory, discrete geometry, and dynamical systems. In particular,…

We give an algorithm to compute a morph between any two convex drawings of the same plane graph. The morph preserves the convexity of the drawing at any time instant and moves each vertex along a piecewise linear curve with linear…

We consider a graph called a lattice diagram, which is a graph in the $xy$-plane such that each edge is parallel to the $x$-axis or the $y$-axis. In [4], we investigated transformations of certain lattice diagrams, and we considered the…

These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…

We study the cutwidth measure on graphs and ways to bound the cutwidth of a graph by partitioning its vertices. We consider bounds expressed as a function of two quantities: on the one hand, the maximal cutwidth y of the subgraphs induced…

Graph partitioning, or the dividing of a graph into two or more parts based on certain conditions, arises naturally throughout discrete mathematics, and problems of this kind have been studied extensively. In the 1990s, Ando conjectured…

We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…