Related papers: Reconstruction of small graphs and digraphs
We investigate a cops and robber game on directed graphs, where the robber moves along the arcs of the graph, while the cops can select any position at each time step. Our main focus is on the cop number: the minimum number of cops required…
We study here the graphs with seven vertices in an effort to classify which of them appear as the prime character degree graphs of finite solvable groups. This classification is complete for the disconnected graphs. Of the 853…
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…
Reconfiguration graphs provide a way to represent relationships among solutions to a problem, and have been studied in many contexts. We investigate the reconfiguration graphs corresponding to minimum PSD forcing sets and minimum skew…
Local Irregularity Conjecture states that every simple connected graph, except special cacti, can be decomposed into at most three locally irregular graphs, i.e., graphs in which adjacent vertices have different degrees. The connected…
We consider the problem of decomposing the edges of a digraph into as few paths as possible. A natural lower bound for the number of paths in any path decomposition of a digraph $D$ is $\frac{1}{2}\sum_{v\in V(D)}|d^+(v)-d^-(v)|$; any…
The graph reconstruction problem has been extensively studied under various query models. In this paper, we propose a new query model regarding the number of connected components, which is one of the most basic and fundamental graph…
Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present an evolutionary algorithm for reconstruction of…
This paper develops an algorithm that identifies and decomposes a median graph of a triangulation of a 2-dimensional (2D) oriented bordered surface and in addition restores all corresponding triangulation whenever they exist. The algorithm…
For every ordered set, we reconstruct the deck obtained by removal of the elements of rank r that are neither minimal nor maximal. Consequently, we also reconstruct the deck obtained by removal of the extremal, that is, minimal or maximal,…
The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…
Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a linear ordering of its vertex set for which their adjacency…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…
We discuss weak and strong links (`virtual connections') in the Shannon game. General properties of these links are discussed, leading to a method to find all links of given size by a suitably pruned exhaustive search. This is applied to…
A digraph $D$ is $k$-linked if for every $2k$ distinct vertices $ x_1,\ldots , x_k, y_1, \ldots , y_k$ in $D$, there exist $k$ pairwise vertex-disjoint paths $P_1,\ldots, P_k$ such that $P_i$ starts at $x_i$ and ends at $y_i$ for each $i\in…
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
In this paper, we prove that, for every graph with at least 5 vertices, one can delete at most 3 vertices such that the subgraph obtained has at least three vertices with the same degree. This solves an open problem of Caro, Shapira and…
We are developing an interactive graph exploration system called Graph Playground for making sense of large graphs. Graph Playground offers a fast and scalable edge decomposition algorithm, based on iterative vertex-edge peeling, to…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…