{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:01Z","timestamp":1753889881561,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T00:00:00Z","timestamp":1562544000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T00:00:00Z","timestamp":1562544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T00:00:00Z","timestamp":1562544000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We show that the class of chordal claw-free graphs admits LREC$_=$-definable canonization. LREC$_=$ is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm, and therefore a logarithmic-space isomorphism test, for the class of chordal claw-free graphs. As a further consequence, LREC$_=$ captures logarithmic space on this graph class. Since LREC$_=$ is contained in fixed-point logic with counting, we also obtain that fixed-point logic with counting captures polynomial time on the class of chordal claw-free graphs.<\/jats:p><jats:p>Comment: 34 pages, 13 figures<\/jats:p>","DOI":"10.23638\/lmcs-15(3:2)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:37:15Z","timestamp":1743701835000},"source":"Crossref","is-referenced-by-count":0,"title":["Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs"],"prefix":"10.23638","volume":"Volume 15, Issue 3","author":[{"given":"Berit","family":"Gru\u00dfien","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,7,8]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1802.10331v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1802.10331v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:37:15Z","timestamp":1743701835000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4333"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,8]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(3:2)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1802.10331v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1802.10331v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1802.10331v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1802.10331","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1802.10331","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2019,7,8]]},"article-number":"4333"}}