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Random Graphs with Forbidden Vertex Degrees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2010 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 37, no 2, 137-175 p.Article in journal (Refereed) Published
Abstract [en]

We study the random graph G 4 conditioned on the event that all vertex degrees he in some given subset S of the nonnegative interacts. Subject to a certain hypothesis on S. the empirical distribution of the vertex degrees is asymptotically Poisson with some parameter (mu) over cap men as the root of a certain "characteristic equation" of S that maximizes a certain function psi s(mu) Subject to a hypothesis on S. we obtain a partial description of the structure of such a random graph, including a condition for the existence (or not) of a giant component The requisite hypothesis is in many cases benign. and applications are presented to a number of choices for the set S including the sets of (respectively) even and odd numbers.

Place, publisher, year, edition, pages
2010. Vol. 37, no 2, 137-175 p.
Keyword [en]
random graph, even graph, random-cluster model
National Category
URN: urn:nbn:se:uu:diva-135193DOI: 10.1002/rsa.20307ISI: 000281045300001OAI: oai:DiVA.org:uu-135193DiVA: diva2:374688
Available from: 2010-12-06 Created: 2010-12-06 Last updated: 2011-03-01Bibliographically approved

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