The number of Euler tours of a random $d$-in/$d$-out graph

Abstract : In this paper we obtain the expectation and variance of the number of Euler tours of a random $d$-in/$d$-out directed graph, for $d \geq 2$. We use this to obtain the asymptotic distribution and prove a concentration result. We are then able to show that a very simple approach for uniform sampling or approximately counting Euler tours yields algorithms running in expected polynomial time for almost every $d$-in/$d$-out graph. We make use of the BEST theorem of de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte, which shows that the number of Euler tours of a $d$-in/$d$-out graph is the product of the number of arborescences and the term $[(d-1)!]^n/n$. Therefore most of our effort is towards estimating the asymptotic distribution of the number of arborescences of a random $d$-in/$d$-out graph.
Type de document :
Communication dans un congrès
Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.117-128, 2010, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [17 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01185585
Contributeur : Coordination Episciences Iam <>
Soumis le : jeudi 20 août 2015 - 16:33:14
Dernière modification le : jeudi 26 octobre 2017 - 16:34:02
Document(s) archivé(s) le : mercredi 26 avril 2017 - 09:57:25

Fichier

dmAM0109.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Licence


Distributed under a Creative Commons Paternité 4.0 International License

Identifiants

  • HAL Id : hal-01185585, version 1

Collections

Citation

Páidí Creed, Mary Cryan. The number of Euler tours of a random $d$-in/$d$-out graph. Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.117-128, 2010, DMTCS Proceedings. 〈hal-01185585〉

Partager

Métriques

Consultations de la notice

96

Téléchargements de fichiers

52