{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841023,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>An $({\\cal I},{\\cal F}_d)$-partition of a graph is a partition of the vertices of the graph into two sets $I$ and $F$, such that $I$ is an independent set and $F$ induces a forest of maximum degree at most $d$.\u00a0We show that for all $M&lt;3$ and $d \\ge \\frac{2}{3-M} - 2$, if a graph has maximum average degree less than $M$, then it has an $({\\cal I},{\\cal F}_d)$-partition. Additionally, we prove that for all $\\frac{8}{3} \\le M &lt; 3$ and $d \\ge \\frac{1}{3-M}$, if a graph has maximum average degree less than $M$ then it has an $({\\cal I},{\\cal F}_d)$-partition. It follows that planar graphs with girth at least $7$ (resp. $8$, $10$) admit an $({\\cal I},{\\cal F}_5)$-partition (resp. $({\\cal I},{\\cal F}_3)$-partition, $({\\cal I},{\\cal F}_2)$-partition).<\/jats:p>","DOI":"10.37236\/6815","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:37:19Z","timestamp":1578670639000},"source":"Crossref","is-referenced-by-count":3,"title":["Partitioning Sparse Graphs into an Independent Set and a Forest of Bounded Degree"],"prefix":"10.37236","volume":"25","author":[{"given":"Fran\u00e7ois","family":"Dross","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mickael","family":"Montassier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandre","family":"Pinlou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2018,3,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p45\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p45\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:38:02Z","timestamp":1579235882000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.37236\/6815","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,2]]},"article-number":"P1.45"}}