Related papers: Vertex Collapsing and Cut Ideals
In this paper we study fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. To prepare the ground, we define various types of subhypergraphs, as…
We present a parallel version of the cut-pursuit algorithm for minimizing functionals involving the graph total variation. We show that the decomposition of the iterate into constant connected components, which is at the center of this…
There is a well-documented research programme on graph operators which addresses questions such as `Which graphs appear as images of graphs?'; `Which graphs are fixed under the operator?'; `What happens if the operator is iterated?' In this…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
Let $G$ be a finite graph on $[n]:=\{1, \ldots, n\}$ and $\kappa(G)$ its vertex connectivity. Let $S=K[x_1, \ldots, x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I(G^c)$ the edge ideal of the complementary graph…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
Bispanning graphs are undirected graphs with an edge set that can be decomposed into two disjoint spanning trees. The operation of symmetrically swapping two edges between the trees, such that the result is a different pair of disjoint…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Given a set of nonempty subsets of some universal set, their intersection graph is defined as the graph with one vertex for each set and two vertices are adjacent precisely when their representing sets have non-empty intersection. Sometimes…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with…
One version of Whitehead's famous cut vertex lemma says that if an element of a free group is part of a free basis, then a certain graph associated to its conjugacy class that we call the star graph is either disconnected or has a cut…
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,…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
We study the problem of deleting the smallest set $S$ of vertices (resp. edges) from a given graph $G$ such that the induced subgraph (resp. subgraph) $G \setminus S$ belongs to some class $\mathcal{H}$. We consider the case where graphs in…
The splitting number is effective to distinguish the embedded topology of plane curves, and it is not determined by the fundamental group of the complement of the plane curve. In this paper, we give a generalization of the splitting number,…
Cut vertices, a generalization of matrix elements of local operators, are revisited, and an expansion in terms of minimally subtracted cut vertices is formulated. An extension of the formalism to deal with semi-inclusive deep inelastic…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…