Let G be chosen uniformly at random from the set G G r, n of r-regular graphs w x Ε½ . with vertex set n . We describe polynomial time algorithms that whp i find a Ε½ . Hamilton cycle in G, and ii approximately count the number of Hamilton cycles in G.
Generating Random Regular Graphs
β Scribed by J. H. Kim; V. H. Vu*
- Publisher
- Springer-Verlag
- Year
- 2006
- Tongue
- English
- Weight
- 325 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0209-9683
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π SIMILAR VOLUMES
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
## Abstract For __k__=0, 1, 2, 3, 4, 5, let ${\cal{P}}\_{k}$ be the class of __k__ βedgeβconnected 5βregular planar graphs. In this paper, graph operations are introduced that generate all graphs in each ${\cal{P}}\_{k}$. Β© 2009 Wiley Periodicals, Inc. J Graph Theory 61: 219β240, 2009
Strongly regular graphs lie on the cusp between highly structured and unstructured. For example, there is a unique strongly regular graph with parameters (36; 10; 4; 2), but there are 32548 non-isomorphic graphs with parameters (36; 15; 6; 6). (The ΓΏrst assertion is a special case of a theorem of Sh