Related papers: Hamilton Cycles in Random Graphs: a bibliography

Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if $p\ge(\log n+\omega(1))/n$ then D(n,p) typically has a…

We first fully implement, in Maple, the ingenious method of Robert Stoyan and Volker Strehl from 1995 to automatically derive generating functions for the number of Hamiltonian cycles in an m by n grid graph ,for a fixed width m, but…

We study the computational complexity of Feedback Vertex Set on subclasses of Hamiltonian graphs. In particular, we consider Hamiltonian graphs that are regular or are planar and regular. Moreover, we study the less known class of…

We provide sufficient conditions for the existence of long cycles in locally expanding graphs, and present applications of our conditions and techniques to Ramsey theory, random graphs and positional games.

Let $H_{n,p,r}^{(k)}$ denote a randomly colored random hypergraph, constructed on the vertex set $[n]$ by taking each $k$-tuple independently with probability $p$, and then independently coloring it with a random color from the set $[r]$.…

In this short note, we give a description of the Parry-Sullivan number of a graph in terms of the cycles in the graph. This tool is occasionally useful in reasoning about the Parry-Sullivan numbers of graphs.

We count cycles of an unbounded length in generalized Johnson graphs. Asymptotics of the number of such cycles is obtained for certain growth rates of the cycle length.

Let D be the circulant digraph with n vertices and connection set {2,3,c}. (Assume D is loopless and has outdegree 3.) Work of S.C.Locke and D.Witte implies that if n is a multiple of 6, c is either (n/2) + 2 or (n/2) + 3, and c is even,…

Given a finite abelian group $G$, consider the complete graph on the set of all elements of $G$. Find a Hamiltonian cycle in this graph and for each pair of consecutive vertices along the cycle compute their sum. What are the smallest and…

Motivated to find the answers to some of the questions that have occurred in recent papers dealing with Hamiltonian cycles (abbreviated HCs) in some special classes of grid graphs we started the investigation of spanning unions of cycles,…

The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum…

If the line graph of a graph $G$ decomposes into Hamiltonian cycles, what is $G$? We answer this question for decomposition into two cycles.

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…

Let $H_r(n,p)$ denote the maximum number of Hamiltonian cycles in an $n$-vertex $r$-graph with density $p \in (0,1)$. The expected number of Hamiltonian cycles in the random $r$-graph model $G_r(n,p)$ is $E(n,p)=p^n(n-1)!/2$ and in the…

Some years ago I demonstrated a simulated annealing heuristic for the Hamiltonian cycle problem (Science 273, 413 (1996)). Here I propose an improved version of this heuristic.

We study the statistics of Hamiltonian cycles on various families of bicolored random planar maps (with the spherical topology). These families fall into two groups corresponding to two distinct universality classes with respective central…

We state and prove a correct version of a theorem presented in an earlier paper.

We associate each endomorphism of a finite cyclic group with a digraph and study many properties of this digraph, including its adjacent matrix and automorphism group.

We present a deterministic algorithm that given any directed graph on n vertices computes the parity of its number of Hamiltonian cycles in O(1.619^n) time and polynomial space. For bipartite graphs, we give a 1.5^n poly(n) expected time…

Finding Hamitonian Cycles in square grid graphs is a well studied and important questions. More recent work has extended these results to triangular and hexagonal grids, as well as further restricted versions. In this paper, we examine a…