Related papers: Obtaining hamilton cicuits in graphs and digraphs

Consider the random graph process where we start with an empty graph on n vertices, and at time t, are given an edge e_t chosen uniformly at random among the edges which have not appeared so far. A classical result in random graph theory…

We prove a conjecture of Penrose about the standard random geometric graph process, in which n vertices are placed at random on the unit square and edges are sequentially added in increasing order of lengths taken in the l_p norm. We show…

We discuss several classical results about long paths and Hamilton cycles in random graphs and present accessible versions of their proofs, relying on the Depth First Search (DFS) algorithm and the notion of boosters.

In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic…

Let $G$ be a regular graph and $H$ a subgraph on the same vertex set. We give surprisingly compact formulas for the number of copies of $H$ one expects to find in a random subgraph of $G$.

We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…

In here, I present a series of combinatorial equalities derived using a graph based approach. Different nodes in the graphs are visited following probabilistic dynamics of a moving dot. The results are presented in such a way that the…

We prove that a random graph $G(n,p)$, with $p$ above the Hamiltonicity threshold, is typically such that for any $r$-colouring of its edges there exists a Hamilton cycle with at least $(2/(r+ 1)-o(1))n$ edges of the same colour. This…

Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is usually no standard set of instances to benchmark performance. Second, using existing graph generators results in a…

In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…

Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…

Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…

We describe a practical algorithm to compute the (oriented) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algorithms. The aim of this algorithm is to be fast enough for…

One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a truly random one. In the context of graphs, Chung, Graham, and Wilson…

We focus on the algorithm underlying the main result of [A. Mestre, R. Oeckl, Generating loop graphs via Hopf algebra in quantum field theory. J. Math. Phys., 47, 122302, 2006]. This is an algebraic formula to generate all connected graphs…

This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections…

In this paper, we study the Hamiltonicity of graphs with large minimum degree. Firstly, we present some conditions for a simple graph to be Hamilton-connected and traceable from every vertex in terms of the spectral radius of the graph or…

This paper shows NP-completeness for finding Hamiltonian cycles in induced subgraphs of the dual graphs of semi-regular tessilations. It also shows NP-hardness for a new, wide class of graphs called augmented square grids. This work follows…

In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex…

We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a…