The Pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is True

We prove that for any positive integers \(k\) and \(d\), if a graph \(G\) has maximum average degree at most \(2k + \frac{2d}{d+k+1}\), then \(G\) decomposes into \(k+1\) pseudoforests \(C_{1},\ldots,C_{k+1}\) such that there is an \(i\) such that for every connected component \(C\) of \(C_{i}\), we...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-07
Main Authors: Grout, Logan, Moore, Benjamin
Format: Article
Language:English
Subjects:
Integers
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Grout, Logan
Moore, Benjamin
description We prove that for any positive integers \(k\) and \(d\), if a graph \(G\) has maximum average degree at most \(2k + \frac{2d}{d+k+1}\), then \(G\) decomposes into \(k+1\) pseudoforests \(C_{1},\ldots,C_{k+1}\) such that there is an \(i\) such that for every connected component \(C\) of \(C_{i}\), we have that \(e(C) \leq d\).
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2221584079</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2221584079</sourcerecordid><originalsourceid>FETCH-proquest_journals_22215840793</originalsourceid><addsrcrecordid>eNqNjM0KgkAUhYcgSMp3uNBaGO9o2tqKFhFB7mWoqykyt-bn_ZtFD9DqcM53-BYiQaXyrC4QVyJ1bpJS4q7CslSJuLQvgpuj8OSeLTkP2uiZh0AQO_hI796yGeA6GoKD1QMbaC0RNGwmevhgCUYXp0Absez17Cj95VpsT8e2OWdvy58Q5d3EwUa_6xAxL-tCVnv13-sLFp08-Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2221584079</pqid></control><display><type>article</type><title>The Pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is True</title><source>Publicly Available Content (ProQuest)</source><creator>Grout, Logan ; Moore, Benjamin</creator><creatorcontrib>Grout, Logan ; Moore, Benjamin</creatorcontrib><description>We prove that for any positive integers \(k\) and \(d\), if a graph \(G\) has maximum average degree at most \(2k + \frac{2d}{d+k+1}\), then \(G\) decomposes into \(k+1\) pseudoforests \(C_{1},\ldots,C_{k+1}\) such that there is an \(i\) such that for every connected component \(C\) of \(C_{i}\), we have that \(e(C) \leq d\).</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Integers</subject><ispartof>arXiv.org, 2020-07</ispartof><rights>2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2221584079?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25753,37012,44590</link.rule.ids></links><search><creatorcontrib>Grout, Logan</creatorcontrib><creatorcontrib>Moore, Benjamin</creatorcontrib><title>The Pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is True</title><title>arXiv.org</title><description>We prove that for any positive integers \(k\) and \(d\), if a graph \(G\) has maximum average degree at most \(2k + \frac{2d}{d+k+1}\), then \(G\) decomposes into \(k+1\) pseudoforests \(C_{1},\ldots,C_{k+1}\) such that there is an \(i\) such that for every connected component \(C\) of \(C_{i}\), we have that \(e(C) \leq d\).</description><subject>Integers</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNjM0KgkAUhYcgSMp3uNBaGO9o2tqKFhFB7mWoqykyt-bn_ZtFD9DqcM53-BYiQaXyrC4QVyJ1bpJS4q7CslSJuLQvgpuj8OSeLTkP2uiZh0AQO_hI796yGeA6GoKD1QMbaC0RNGwmevhgCUYXp0Absez17Cj95VpsT8e2OWdvy58Q5d3EwUa_6xAxL-tCVnv13-sLFp08-Q</recordid><startdate>20200705</startdate><enddate>20200705</enddate><creator>Grout, Logan</creator><creator>Moore, Benjamin</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20200705</creationdate><title>The Pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is True</title><author>Grout, Logan ; Moore, Benjamin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_22215840793</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Integers</topic><toplevel>online_resources</toplevel><creatorcontrib>Grout, Logan</creatorcontrib><creatorcontrib>Moore, Benjamin</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Grout, Logan</au><au>Moore, Benjamin</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>The Pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is True</atitle><jtitle>arXiv.org</jtitle><date>2020-07-05</date><risdate>2020</risdate><eissn>2331-8422</eissn><abstract>We prove that for any positive integers \(k\) and \(d\), if a graph \(G\) has maximum average degree at most \(2k + \frac{2d}{d+k+1}\), then \(G\) decomposes into \(k+1\) pseudoforests \(C_{1},\ldots,C_{k+1}\) such that there is an \(i\) such that for every connected component \(C\) of \(C_{i}\), we have that \(e(C) \leq d\).</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2020-07
issn 2331-8422
language eng
recordid cdi_proquest_journals_2221584079
source Publicly Available Content (ProQuest)
subjects Integers
title The Pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is True
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T00%3A17%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=The%20Pseudoforest%20analogue%20for%20the%20Strong%20Nine%20Dragon%20Tree%20Conjecture%20is%20True&rft.jtitle=arXiv.org&rft.au=Grout,%20Logan&rft.date=2020-07-05&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2221584079%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_22215840793%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2221584079&rft_id=info:pmid/&rfr_iscdi=true