Counting Connected Graphs Asymptotically

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dc.creatorvan der Hofstad, Remco
dc.creatorSpencer, Joel
dc.date2005-02-28
dc.date.accessioned2026-07-07T05:17:33Z
dc.date.available2026-07-07T05:17:33Z
dc.descriptionWe find the asymptotic number of connected graphs with $k$ vertices and $k-1+l$ edges when $k,l$ approach infinity, reproving a result of Bender, Canfield and McKay. We use the {\em probabilistic method}, analyzing breadth-first search on the random graph $G(k,p)$ for an appropriate edge probability $p$. Central is analysis of a random walk with fixed beginning and end which is tilted to the left.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0502579
dc.identifierhttp://arxiv.org/abs/math/0502579
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74343
dc.subjectCombinatorics
dc.subjectProbability
dc.titleCounting Connected Graphs Asymptotically
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