Chordal graphs with bounded tree-width
Given t≥2 and 0≤k≤t, we prove that the number of labelled k-connected chordal graphs with n vertices and tree-width at most t is asymptotically cn−5/2γnn!, as n→∞, for some constants c,γ>0 depending on t and k. Additionally, we show that the number of i-cliques (2≤i≤t) in a uniform random k-conne...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/537574 |
| Acceso en línea: | http://hdl.handle.net/2072/537574 |
| Access Level: | acceso abierto |
| Palabra clave: | Chordal Graphs, Bounded tree-width |
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oai:recercat.cat:2072/537574 |
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Chordal graphs with bounded tree-width Castellví, J. Drmota, M. Noy, M. Requilé, C. Chordal Graphs, Bounded tree-width Given t≥2 and 0≤k≤t, we prove that the number of labelled k-connected chordal graphs with n vertices and tree-width at most t is asymptotically cn−5/2γnn!, as n→∞, for some constants c,γ>0 depending on t and k. Additionally, we show that the number of i-cliques (2≤i≤t) in a uniform random k-connected chordal graph with tree-width at most t is normally distributed as n→∞. The asymptotic enumeration of graphs of tree-width at most t is wide open for t≥3. To the best of our knowledge, this is the first non-trivial class of graphs with bounded tree-width where the asymptotic counting problem is solved. Our starting point is the work of Wormald (1985) [21], were an algorithm is developed to obtain the exact number of labelled chordal graphs on n vertices. © 2024 Elsevier Inc. The authors acknowledge support from the Marie Curie RISE research network “RandNet” MSCA-RISE-2020-101007705. Moreover, M.D. was supported by the Special Research Program SFB F50-02 “Algorithmic and Enumerative Combinatorics”, and by the project P35016 “Infinite Singular Systems and Random Discrete Objects” of the FWF (Austrian Science Fund). Additionally, M.N. and C.R. acknowledge the financial support of the Spanish State Research Agency through projects MTM2017-82166-P and PID2020-113082GB-I00, while M.N. acknowledges support from the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence (CEX2020-001084-M), and C.R. acknowledges support from the grant Beatriu de Pinós BP2019, funded by the H2020 COFUND project No 801370 and AGAUR (the Catalan agency for management of university and research grants). Academic Press Inc. http://hdl.handle.net/2072/537574 |
| title |
Chordal graphs with bounded tree-width |
| spellingShingle |
Chordal graphs with bounded tree-width Castellví, J. Chordal Graphs, Bounded tree-width |
| title_short |
Chordal graphs with bounded tree-width |
| title_full |
Chordal graphs with bounded tree-width |
| title_fullStr |
Chordal graphs with bounded tree-width |
| title_full_unstemmed |
Chordal graphs with bounded tree-width |
| title_sort |
Chordal graphs with bounded tree-width |
| author |
Castellví, J. |
| author_facet |
Castellví, J. Drmota, M. Noy, M. Requilé, C. |
| author_role |
author |
| author2 |
Drmota, M. Noy, M. Requilé, C. |
| author2_role |
author author author |
| topic |
Chordal Graphs, Bounded tree-width |
| topic_facet |
Chordal Graphs, Bounded tree-width |
| description |
Given t≥2 and 0≤k≤t, we prove that the number of labelled k-connected chordal graphs with n vertices and tree-width at most t is asymptotically cn−5/2γnn!, as n→∞, for some constants c,γ>0 depending on t and k. Additionally, we show that the number of i-cliques (2≤i≤t) in a uniform random k-connected chordal graph with tree-width at most t is normally distributed as n→∞. The asymptotic enumeration of graphs of tree-width at most t is wide open for t≥3. To the best of our knowledge, this is the first non-trivial class of graphs with bounded tree-width where the asymptotic counting problem is solved. Our starting point is the work of Wormald (1985) [21], were an algorithm is developed to obtain the exact number of labelled chordal graphs on n vertices. © 2024 Elsevier Inc. |
| publishDate |
2024 |
| format |
article |
| status_str |
acceptedVersion |
| url |
http://hdl.handle.net/2072/537574 |
| eu_rights_str_mv |
openAccess |
| publisher |
Academic Press Inc. |
| institution |
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| collection |
Recercat. Dipósit de la Recerca de Catalunya |
| reponame_str |
Recercat. Dipósit de la Recerca de Catalunya |
| instname_str |
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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1878737374637195264 |
| publishDateSort |
2024 |
| author_browse |
Castellví, J. Drmota, M. Noy, M. Requilé, C. |
| publisherStr |
Academic Press Inc. |
| score |
6.8972664 |