Systems engineers have recently shown interest in algorithms for drawing directed graphs so that they are easy to understand and remember. Each of the commonly used methods has a step which aims toâ€¦ (More)

This is a survey of results on properties of random regular graphs, together with an exposition of some of the main methods of obtaining these results. Related results on asymptotic enumeration areâ€¦ (More)

We determine the asymptotic number of labelled graphs with a given degree sequence for the case where the maximum degree is o(|E(G)|). The previously best enumeration, by the first author, requiredâ€¦ (More)

We derive the asymptotic expression for the number of labeled 2-connected planar graphs with respect to vertices and edges. We also show that almost all such graphs with n vertices contain manyâ€¦ (More)

There are various algorithms known for generating graphs with n vertices of given degrees uniformly at random. Unfortunately, none of them is of practical use for all degree sequences, even for thoseâ€¦ (More)

Minimal perfect hash functions are used for memory efficient storage and fast retrieval of items from static sets. We present an infinite family of efficient and practical algorithms for generatingâ€¦ (More)

We show how to generate k-regular graphs on n vertices uniformly at random in expected time O(nk3), provided k = O(n1/3). The algorithm employs a modification of a switching argument previously usedâ€¦ (More)