Related papers: Reconstruction of small graphs and digraphs
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…
The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem of reconstructing a random $d$-uniform hypergraph from its…
Multiple methods of finding the vertices belonging to a planted dense subgraph in a random dense $G(n, p)$ graph have been proposed, with an emphasis on planted cliques. Such methods can identify the planted subgraph in polynomial time, but…
A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood and the in-neighbourhood of any vertex induce a semicomplete digraph. In this paper we study various…
We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph $G$ is a set $S$ of vertices such that each vertex is either in $S$ or has a neighbour in $S$. In a reconfiguration problem, the goal is…
In this paper, an effort is made to classify which prime character degree graphs having eight vertices occur for some finite solvable group. To approach this, we compile known results and constructions from the literature which are used to…
The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a…
The problem of graph reconstruction has been studied in its various forms over the years. In particular, the Reconstruction Conjecture, proposed by Ulam and Kelly in 1942, has attracted much research attention and yet remains one of the…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
Graph neural networks (GNNs) have limited expressive power, failing to represent many graph classes correctly. While more expressive graph representation learning (GRL) alternatives can distinguish some of these classes, they are…
We introduce the cycle intersection graph of a graph, an adaptation of the cycle graph of a graph, and use the structure of these graphs to prove an upper bound for the decycling number of all even graphs. This bound is shown to be…
Gallai's path decomposition conjecture states that the edges of any connected graph on n vertices can be decomposed into at most (n+1)/2 paths. We confirm that conjecture for all graphs with maximum degree at most five.
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.…
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances. In this…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
We study in how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator…
We study biplane graphs drawn on a finite point set $S$ in the plane in general position. This is the family of geometric graphs whose vertex set is $S$ and which can be decomposed into two plane graphs. We show that every sufficiently…
Extending a classic result of Johnson and Newman, this paper provides a matrix characterization for two generalized cospectral graphs with a pair of generalized cospectral vertex-deleted subgraphs. As an application, we present a new…
We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an…
Let $\mathcal{Q}$ be a vertex subset problem on graphs. In a reconfiguration variant of $\mathcal{Q}$ we are given a graph $G$ and two feasible solutions $S_s, S_t\subseteq V(G)$ of $\mathcal{Q}$ with $|S_s|=|S_t|=k$. The problem is to…