On disjoint hypercubes in Fibonacci cubes

On disjoint hypercubes in Fibonacci cubes

The Fibonacci cube of dimension n, denoted as Γn, is the subgraph of n-cube Qn induced by vertices with no consecutive 1’s. We study the maximum number of disjoint subgraphs in Γn isomorphic to Qk, and denote this number by qk(n). We prove several recursive results for qk(n), in particular we prove...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Discrete Applied Mathematics 2015-08, Vol.190-191, p.50-55
Hauptverfasser: Gravier, Sylvain, Mollard, Michel, Špacapan, Simon, Zemljič, Sara Sabrina
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Fibonacci cube
Fibonacci numbers
Mathematics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 55
container_issue
container_start_page 50
container_title Discrete Applied Mathematics
container_volume 190-191
creator Gravier, Sylvain
Mollard, Michel
Špacapan, Simon
Zemljič, Sara Sabrina
description The Fibonacci cube of dimension n, denoted as Γn, is the subgraph of n-cube Qn induced by vertices with no consecutive 1’s. We study the maximum number of disjoint subgraphs in Γn isomorphic to Qk, and denote this number by qk(n). We prove several recursive results for qk(n), in particular we prove that qk(n)=qk−1(n−2)+qk(n−3). We also prove a closed formula in which qk(n) is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence {qk(n)}n=0∞.
doi_str_mv 10.1016/j.dam.2015.03.016
format Article
fullrecord <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_01139094v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0166218X15001651</els_id><sourcerecordid>oai_HAL_hal_01139094v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c444t-811a94c02767d57a00b9a0c3d46109a20eed94ffd21ae5c121a0d8df694ce4ea3</originalsourceid><addsrcrecordid>eNp9kMFKw0AQhhdRsFYfwFuuPSTOJNtNgqdSrBUCvSh4W6a7E7qhTcpuLfTt3Vrx6GmYj_mGmV-IR4QMAdVTl1naZTngNIMii-RKjLAq81SVJV6LUSQqzbH6vBV3IXQAgLEbicmqT6wL3eD6Q7I57dmbrzWHxPXJwq2HnoxxyQ-6FzctbQM__Nax-Fi8vM-XabN6fZvPmtRIKQ9phUi1NJCXqrTTkgDWNYEprFQINeXAbGvZtjZH4qmJVxDYyrYqSiyZirGYXPZuaKv33u3In_RATi9njT4zQCxqqOUR4yxeZo0fQvDc_gkI-pyL7nTMRZ9z0VBEVUXn-eJwfOLo2OtgHPeGrfNsDtoO7h_7G5nVaTw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On disjoint hypercubes in Fibonacci cubes</title><source>Elsevier ScienceDirect Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Gravier, Sylvain ; Mollard, Michel ; Špacapan, Simon ; Zemljič, Sara Sabrina</creator><creatorcontrib>Gravier, Sylvain ; Mollard, Michel ; Špacapan, Simon ; Zemljič, Sara Sabrina</creatorcontrib><description>The Fibonacci cube of dimension n, denoted as Γn, is the subgraph of n-cube Qn induced by vertices with no consecutive 1’s. We study the maximum number of disjoint subgraphs in Γn isomorphic to Qk, and denote this number by qk(n). We prove several recursive results for qk(n), in particular we prove that qk(n)=qk−1(n−2)+qk(n−3). We also prove a closed formula in which qk(n) is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence {qk(n)}n=0∞.</description><identifier>ISSN: 0166-218X</identifier><identifier>EISSN: 1872-6771</identifier><identifier>DOI: 10.1016/j.dam.2015.03.016</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Combinatorics ; Fibonacci cube ; Fibonacci numbers ; Mathematics</subject><ispartof>Discrete Applied Mathematics, 2015-08, Vol.190-191, p.50-55</ispartof><rights>2015</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c444t-811a94c02767d57a00b9a0c3d46109a20eed94ffd21ae5c121a0d8df694ce4ea3</citedby><cites>FETCH-LOGICAL-c444t-811a94c02767d57a00b9a0c3d46109a20eed94ffd21ae5c121a0d8df694ce4ea3</cites><orcidid>0000-0003-2859-275X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0166218X15001651$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>230,314,776,780,881,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01139094$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Gravier, Sylvain</creatorcontrib><creatorcontrib>Mollard, Michel</creatorcontrib><creatorcontrib>Špacapan, Simon</creatorcontrib><creatorcontrib>Zemljič, Sara Sabrina</creatorcontrib><title>On disjoint hypercubes in Fibonacci cubes</title><title>Discrete Applied Mathematics</title><description>The Fibonacci cube of dimension n, denoted as Γn, is the subgraph of n-cube Qn induced by vertices with no consecutive 1’s. We study the maximum number of disjoint subgraphs in Γn isomorphic to Qk, and denote this number by qk(n). We prove several recursive results for qk(n), in particular we prove that qk(n)=qk−1(n−2)+qk(n−3). We also prove a closed formula in which qk(n) is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence {qk(n)}n=0∞.</description><subject>Combinatorics</subject><subject>Fibonacci cube</subject><subject>Fibonacci numbers</subject><subject>Mathematics</subject><issn>0166-218X</issn><issn>1872-6771</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKw0AQhhdRsFYfwFuuPSTOJNtNgqdSrBUCvSh4W6a7E7qhTcpuLfTt3Vrx6GmYj_mGmV-IR4QMAdVTl1naZTngNIMii-RKjLAq81SVJV6LUSQqzbH6vBV3IXQAgLEbicmqT6wL3eD6Q7I57dmbrzWHxPXJwq2HnoxxyQ-6FzctbQM__Nax-Fi8vM-XabN6fZvPmtRIKQ9phUi1NJCXqrTTkgDWNYEprFQINeXAbGvZtjZH4qmJVxDYyrYqSiyZirGYXPZuaKv33u3In_RATi9njT4zQCxqqOUR4yxeZo0fQvDc_gkI-pyL7nTMRZ9z0VBEVUXn-eJwfOLo2OtgHPeGrfNsDtoO7h_7G5nVaTw</recordid><startdate>20150820</startdate><enddate>20150820</enddate><creator>Gravier, Sylvain</creator><creator>Mollard, Michel</creator><creator>Špacapan, Simon</creator><creator>Zemljič, Sara Sabrina</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0003-2859-275X</orcidid></search><sort><creationdate>20150820</creationdate><title>On disjoint hypercubes in Fibonacci cubes</title><author>Gravier, Sylvain ; Mollard, Michel ; Špacapan, Simon ; Zemljič, Sara Sabrina</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c444t-811a94c02767d57a00b9a0c3d46109a20eed94ffd21ae5c121a0d8df694ce4ea3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Combinatorics</topic><topic>Fibonacci cube</topic><topic>Fibonacci numbers</topic><topic>Mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gravier, Sylvain</creatorcontrib><creatorcontrib>Mollard, Michel</creatorcontrib><creatorcontrib>Špacapan, Simon</creatorcontrib><creatorcontrib>Zemljič, Sara Sabrina</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Discrete Applied Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gravier, Sylvain</au><au>Mollard, Michel</au><au>Špacapan, Simon</au><au>Zemljič, Sara Sabrina</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On disjoint hypercubes in Fibonacci cubes</atitle><jtitle>Discrete Applied Mathematics</jtitle><date>2015-08-20</date><risdate>2015</risdate><volume>190-191</volume><spage>50</spage><epage>55</epage><pages>50-55</pages><issn>0166-218X</issn><eissn>1872-6771</eissn><abstract>The Fibonacci cube of dimension n, denoted as Γn, is the subgraph of n-cube Qn induced by vertices with no consecutive 1’s. We study the maximum number of disjoint subgraphs in Γn isomorphic to Qk, and denote this number by qk(n). We prove several recursive results for qk(n), in particular we prove that qk(n)=qk−1(n−2)+qk(n−3). We also prove a closed formula in which qk(n) is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence {qk(n)}n=0∞.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.dam.2015.03.016</doi><tpages>6</tpages><orcidid>https://orcid.org/0000-0003-2859-275X</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0166-218X
ispartof Discrete Applied Mathematics, 2015-08, Vol.190-191, p.50-55
issn 0166-218X
1872-6771
language eng
recordid cdi_hal_primary_oai_HAL_hal_01139094v1
source Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals
subjects Combinatorics
Fibonacci cube
Fibonacci numbers
Mathematics
title On disjoint hypercubes in Fibonacci cubes
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-30T03%3A39%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20disjoint%20hypercubes%20in%20Fibonacci%20cubes&rft.jtitle=Discrete%20Applied%20Mathematics&rft.au=Gravier,%20Sylvain&rft.date=2015-08-20&rft.volume=190-191&rft.spage=50&rft.epage=55&rft.pages=50-55&rft.issn=0166-218X&rft.eissn=1872-6771&rft_id=info:doi/10.1016/j.dam.2015.03.016&rft_dat=%3Chal_cross%3Eoai_HAL_hal_01139094v1%3C/hal_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_els_id=S0166218X15001651&rfr_iscdi=true