One-factor in random graphs based on vertex choice

On Vertex, Edge, and Vertex-Edge Random Graphs (Extended Abstract)

We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdős-Rényi random graphs [9, 10], vertex random graphs are generalizations of geometric random graphs [21], and vertex-edge random graphs generalize both. The names of these three types of random graphs describe where the randomness in the models lies: in ...

On Vertex, Edge, and Vertex-edge Random Graphs

We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdős-Rényi random graphs [8, 9], vertex random graphs are generalizations of geometric random graphs [20], and vertexedge random graphs generalize both. The names of these three types of random graphs describe where the randomness in the models lies: in th...

Vertex Cover Approximations on Random Graphs

The vertex cover problem is a classical NP-complete problem for which the best worst-case approximation ratio is 2 − o(1). In this paper, we use a collection of simple graph transformations, each of which guarantees an approximation ratio of 3 2 , to find approximate vertex covers for a large collection of randomly generated graphs. These reductions are extremely fast and even though they, by t...

Symmetric Vertex Models on Planar Random Graphs

We discuss a 4-vertex model on an ensemble of 3-valent (Φ) planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The regular lattice equivalent of the model is the symmetric 8-vertex model on the honeycomb lattice, which can be mapped on to an Ising model in field, as was originally shown by Wu et.al. using generalised weak graph transformation technique...

Vertex-Reinforced Random Walk on Arbitrary Graphs