{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T14:51:43Z","timestamp":1774191103249,"version":"3.50.1"},"reference-count":0,"publisher":"Journal of Graph Algorithms and Applications","issue":"1","license":[{"start":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T00:00:00Z","timestamp":1773705600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JGAA"],"abstract":"<jats:p>A common subgraph of two graphs $G_1$ and $G_2$ is a graph that is isomorphic to subgraphs of $G_1$ and $G_2$.\r\nIn the largest common subgraph problem the task is to determine a common subgraph for two given graphs $G_1$ and $G_2$\r\nthat is of maximum possible size ${\\rm lcs}(G_1,G_2)$. This natural problem generalizes the well-studied graph isomorphism problem, has many applications, and remains NP-hard even restricted to unions of paths. We present a simple $4$-approximation algorithm for forests, and, for every fixed $\\epsilon\\in (0,1)$, we show that, for two given forests $F_1$ and $F_2$ of order at most $n$, one can determine in polynomial time a common subgraph $F$ of $F_1$ and $F_2$ with at least ${\\rm lcs}(F_1,F_2)-\\epsilon n$ edges. Restricted to instances with ${\\rm lcs}(F_1,F_2)\\geq cn$ for some fixed positive $c$, this yields a polynomial time approximation scheme. Our approach relies on the approximation of the given forests by structurally simpler forests that are composed of copies of only $O(\\log (n))$ different starlike rooted trees and iterative quantizations of the options for the solutions.<\/jats:p>","DOI":"10.7155\/jgaa.v30i1.2967","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T13:54:33Z","timestamp":1773842073000},"page":"47-63","source":"Crossref","is-referenced-by-count":0,"title":["Largest Common Subgraph of Two Forests"],"prefix":"10.7155","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7214-042X","authenticated-orcid":false,"given":"Dieter","family":"Rautenbach","sequence":"first","affiliation":[]},{"given":"Florian","family":"Werner","sequence":"additional","affiliation":[]}],"member":"4175","published-online":{"date-parts":[[2026,3,17]]},"container-title":["Journal of Graph Algorithms and Applications"],"original-title":[],"link":[{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/download\/2967\/3020","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/download\/2967\/3020","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T13:55:21Z","timestamp":1774187721000},"score":1,"resource":{"primary":{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/view\/2967"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,17]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,17]]}},"URL":"https:\/\/doi.org\/10.7155\/jgaa.v30i1.2967","relation":{},"ISSN":["1526-1719"],"issn-type":[{"value":"1526-1719","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,17]]}}}