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We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

This paper has been withdrawn. (Reason) Its contents have been entirely superseded by the contents of the articles arXiv:0809.3444 and arXiv:0705.3070. There is no profitable reason to keep it alive. No material on it is however wrong.

One interesting question is how a graph develops from some constrained random graph process, which is a fundamental mechanism in the formation and evolution of dynamic networks. The problem here is referred to the random $K_k$-removal…

This paper has been withdrawn by the authors due to a major rewriting.

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This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn by the author due to a crucial problem in Lemma 3. This equation must be changed.

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We study random $k$-connected chordal graphs with bounded tree-width. Our main results are scaling limits and quenched local limits.

This paper has been withdrawn since we combine this paper with math.AC/0503685. All contents of the paper have been moved to math.AC/0503685.