Tree generating regular systems

Generating r-regular graphs

For each nonnegative integer r we determine a set of graph operations such that all r regular loopless graphs can be generated from the smallest r regular loopless graphs by using these operations We also discuss possible extensions of this result to r regular graphs of girth at least g for each xed g

Generating 5-regular planar graphs

For k = 0, 1, 2, 3, 4, 5, let Pk be the class of k-edge-connected 5regular planar graphs. In this paper, graph operations are introduced that generate all graphs in each Pk. ∗Research partially supported by NSF grants DMS-0556091 and ITR-0326387. †Research partially supported by Board of Regents grant LEQSF(2004-07)-RD-A-22.

Generating Random Regular Graphs Quickly

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 those with all degrees equal. In this paper we examine an algorithm which, although it does not generate uniformly at random, is provably close to a uniform generator when the degrees are relatively smal...

Implementing Regular Tree Expressions

Regular tree expressions are a natural formalism for describing the sets of tree-structured values that commonly arise in programs; thus, they are well-suited to applications in program analysis. We describe an implementation of regular tree expressions and our experience with that implementation in the context of the FL type system. A combination of algorithms, optimizations, and fast heuristi...

Regular Tree Model Checking