Finding Hidden Hamiltonian Cycles

On a Simple Randomized Algorithm for Finding Long Cycles in Sparse Graphs

We analyze the performance of a simple randomized algorithm for finding long cycles and 2-factors in directed Hamiltonian graphs of out-degree at most two and in undirected Hamiltonian graphs of degree at most three. For the directed case, the algorithm finds a 2-factor in O(n) expected time. The analysis of our algorithm is based on random walks on a line and interestingly resembles the analys...

On a simple randomized algorithm for finding a 2-factor in sparse graphs

We analyze the performance of a simple randomized algorithm for finding 2-factors in directed Hamiltonian graphs of out-degree at most two and in undirected Hamiltonian graphs of degree at most three. For the directed case, the algorithm finds a 2-factor in O(n) expected time. The analysis of our algorithm is based on random walks on the line and interestingly resembles the analysis of a random...

Mathematics of a Tetrahedron Chain and the Hamiltonian Cycle Problem

In this article we consider the problem of finding Hamiltonian cycles on a tetrahedral mesh. A Hamiltonian cycle is a closed loop through a tetrahedral mesh that visits each tetrahedron exactly once. Using techniques of a novel discrete differential geometry of n-simplices, we could immediately obtain Hamiltonian cycles on a rhombic dodecahedronshaped tetrahedral mesh consisting of 24 tetrahedr...

The Problem of Finding Two Edge-Disjoint Hamiltonian Cycles

Unit-length embedding of cycles and paths on grid graphs

Although there are very algorithms for embedding graphs on unbounded grids, only few results on embedding or drawing graphs on restricted grids has been published. In this work, we consider the problem of embedding paths and cycles on grid graphs. We give the necessary and sufficient conditions for the existence of cycles of given length k and paths of given length k between two given vertices ...