Related papers: Complexity Results in Graph Reconstruction

A graph is said to be a Konig graph if the size of its maximum matching is equal to the size of its minimum vertex cover. The Konig Edge Deletion problem asks if in a given graph there exists a set of at most k edges whose deletion results…

Let $k$ be a fixed integer. We determine the complexity of finding a $p$-partition $(V_1, \dots, V_p)$ of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by $V_i$, ($1\leq i\leq p$) is at…

In this paper we study the problem of testing graph isomorphism (GI) in the CONGEST distributed model. In this setting we test whether the distributive network, $G_U$, is isomorphic to $G_K$ which is given as an input to all the nodes in…

In the Dominated Cluster Deletion problem, we are given an undirected graph $G$ and integers $k$ and $d$ and the question is to decide whether there exists a set of at most $k$ vertices whose removal results in a graph in which each…

Dense subgraph discovery is an important graph-mining primitive with a variety of real-world applications. One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an…

The $k$-deck of a graph is the multiset of its subgraphs induced by $k$ vertices. A graph or graph property is $l$-reconstructible if it is determined by the deck of subgraphs obtained by deleting $l$ vertices. We show that the degree list…

Let $G=(V,E)$ be a simple graph with $|V|=n$ nodes and $|E|=m$ links, a subset $K \subseteq V$ of \emph{terminals}, a vector $p=(p_1,\ldots,p_m) \in [0,1]^m$ and a positive integer $d$, called \emph{diameter}. We assume nodes are perfect…

The problems Cluster Vertex Deletion (or Cluster-VD) and its generalization s-Club Cluster Vertex Deletion (or s-Club-VD, for any integer s>= 1), have been introduced with the aim of detecting highly-connected parts in complex systems.…

Given a simple graph $G = (V, E)$ and a constant integer $k \ge 2$, the $k$-path vertex cover problem ({\sc P$k$VC}) asks for a minimum subset $F \subseteq V$ of vertices such that the induced subgraph $G[V - F]$ does not contain any path…

The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem…

The prevalence of real-world multi-view data makes incomplete multi-view clustering (IMVC) a crucial research. The rapid development of Graph Neural Networks (GNNs) has established them as one of the mainstream approaches for multi-view…

We present an additive $\varepsilon n^{2}$-approximation algorithm for the Graph Edit Distance problem (GED) on graphs of VC dimension $d$ running in time $n^{O(d/\varepsilon^{2})}$. In particular, this recovers a previous result by Arora,…

Degree sequence (DS) problems are around for at least hundred twenty years, and with the advent of network science, more and more complicated, structured DS problems were invented. Interestingly enough all those problems so far are…

The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of…

A graph is locally irregular if no two adjacent vertices have the same degree. The irregular chromatic index $\chi_{\rm irr}'(G)$ of a graph $G$ is the smallest number of locally irregular subgraphs needed to edge-decompose $G$. Not all…

We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the…

The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation…

We study the parameterized complexity of the T(h+1)-Free Edge Deletion problem. Given a graph G and integers k and h, the task is to delete at most k edges so that every connected component of the resulting graph has size at most h. The…

A graph is $\ell$-reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting $\ell$ vertices. We prove that strongly regular graphs with at least six vertices are $2$-reconstructible.

Let $\Pi$ be a hereditary graph class. The problem of deletion to $\Pi$, takes as input a graph $G$ and asks for a minimum number (or a fixed integer $k$) of vertices to be deleted from $G$ so that the resulting graph belongs to $\Pi$. This…