Related papers: A simple Havel-Hakimi type algorithm to realize gr…
We present an algorithm to test whether a given graphical degree sequence is forcibly biconnected or not and prove its correctness. The worst case run time complexity of the algorithm is shown to be exponential but still much better than…
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a k-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily k-connected.
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
For an edge-weighted connected undirected graph, the minimum $k$-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into $k$ connected components. The problem is NP-hard when $k$ is part…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
There are a variety of existing conditions for a degree sequence to be graphic. When a degree sequence satisfies any of these conditions, there exists a graph that realizes the sequence. We formulate several novel sufficient graphicality…
We consider the problem of constructing a graph of minimum degree $k\ge 1$ in the following controlled random graph process, introduced recently by Frieze, Krivelevich and Michaeli. Suppose the edges of the complete graph on $n$ vertices…
We extend our previous algorithm that generates all labeled graphs with a given graphical degree sequence to generate all labeled triangle-free graphs with a given graphical degree sequence. The algorithm uses various pruning techniques to…
We analyse the size of an independent set in a random graph on $n$ vertices with specified vertex degrees, constructed via a simple greedy algorithm: order the vertices arbitrarily, and, for each vertex in turn, place it in the independent…
Complex network is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. The algorithm of horizontal visibility graph (HVG) maps time series into graphs, whose degree distributions are…
The residue of a graph is the number of zeros left after iteratively applying the Havel-Hakimi algorithm to its degree sequence. Favaron, Mah\'{e}o, and Sacl\'{e} showed that the residue is a lower bound on the independence number. The…
Let $G$ be a graph having a vertex $v$ such that $H = G - v$ is a trivially perfect graph. We give a polynomial-time algorithm for the problem of deciding whether it is possible to add at most $k$ edges to $G$ to obtain a trivially perfect…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
We consider the target set selection problem. In this problem, a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least $k$ active neighbors ($k$ is identical for all vertices of…
We describe and analyse a simple greedy algorithm \2G\ that finds a good 2-matching $M$ in the random graph $G=G_{n,cn}^{\d\geq 3}$ when $c\geq 15$. A 2-matching is a spanning subgraph of maximum degree two and $G$ is drawn uniformly from…
Listing all triangles is a fundamental graph operation. Triangles can have important interpretations in real-world graphs, especially social and other interaction networks. Despite the lack of provably efficient (linear, or slightly…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
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…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…