{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:37:41Z","timestamp":1753889861476,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Graph Theory","license":[{"start":{"date-parts":[[2017,10,5]],"date-time":"2017-10-05T00:00:00Z","timestamp":1507161600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,10,5]],"date-time":"2017-10-05T00:00:00Z","timestamp":1507161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,10,5]],"date-time":"2017-10-05T00:00:00Z","timestamp":1507161600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-13-BS02-0007"],"award-info":[{"award-number":["ANR-13-BS02-0007"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Ministry of Education, Science and Technological Development of Republic of Serbia","award":["174033"],"award-info":[{"award-number":["174033"]}]},{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"crossref","award":["EP\/N019660\/1"],"award-info":[{"award-number":["EP\/N019660\/1"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-11-IDEX-0007"],"award-info":[{"award-number":["ANR-11-IDEX-0007"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We present a class of (diamond, even hole)-free graphs with no clique cutset that has unbounded rank-width. In general, even-hole-free graphs have unbounded rank-width, because chordal graphs are even-hole-free. A.A. da Silva, A. Silva and C. Linhares-Sales (2010) showed that planar even-hole-free graphs have bounded rank-width, and N.K. Le (2016) showed that even-hole-free graphs with no star cutset have bounded rank-width. A natural question is to ask, whether even-hole-free graphs with no clique cutsets have bounded rank-width. Our result gives a negative answer. Hence we cannot apply Courcelle and Makowsky's meta-theorem which would provide efficient algorithms for a large number of problems, including the maximum independent set problem, whose complexity remains open for (diamond, even hole)-free graphs.<\/jats:p><jats:p>Comment: 12 pages, 2 figures<\/jats:p>","DOI":"10.23638\/dmtcs-19-1-24","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:40:46Z","timestamp":1743698446000},"source":"Crossref","is-referenced-by-count":0,"title":["On rank-width of even-hole-free graphs"],"prefix":"10.23638","volume":"Vol. 19 no. 1","author":[{"given":"Isolde","family":"Adler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ngoc Khang","family":"Le","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiko","family":"M\u00fcller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marko","family":"Radovanovi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Trotignon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kristina","family":"Vu\u0161kovi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2017,10,5]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1611.09907v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1611.09907v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:40:50Z","timestamp":1743698450000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/2575"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,5]]},"references-count":0,"journal-issue":{"issue":"Graph Theory","published-online":{"date-parts":[[2017,10,5]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-19-1-24","relation":{"has-preprint":[{"id-type":"arxiv","id":"1611.09907v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1611.09907","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1611.09907","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2017,10,5]]},"article-number":"2575"}}