{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:45:22Z","timestamp":1787323522069,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61672536"],"award-info":[{"award-number":["61672536"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972423"],"award-info":[{"award-number":["61972423"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61872048"],"award-info":[{"award-number":["61872048"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61702557"],"award-info":[{"award-number":["61702557"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In 1990, Hendry conjectured that all Hamiltonian chordal graphs are cycle extendable. After a series of papers confirming the conjecture for a number of graph classes, the conjecture is yet refuted by Lafond and Seamone in 2015. Given that their counterexamples are not strongly chordal graphs and they are all only 2-connected, Lafond and Seamone asked the following two questions: (1) Are Hamiltonian strongly chordal graphs cycle extendable? (2) Is there an integer $k$ such that all $k$-connected Hamiltonian chordal graphs are cycle extendable? Later, a conjecture stronger than Hendry's is proposed. In this paper, we resolve all these questions in the negative. On the positive side, we add to the list of cycle-extendable graphs two more graph classes, namely, Hamiltonian 4-fan-free chordal graphs, where every induced $K_5 - e$ has true twins, and Hamiltonian $\\{4{\\sc -fan}, \\overline{A} \\}$-free chordal graphs.<\/jats:p>","DOI":"10.1137\/20m1369920","type":"journal-article","created":{"date-parts":[[2021,9,16]],"date-time":"2021-09-16T10:34:31Z","timestamp":1631788471000},"page":"2115-2128","source":"Crossref","is-referenced-by-count":1,"title":["Cycle Extendability of Hamiltonian Strongly Chordal Graphs"],"prefix":"10.1137","volume":"35","author":[{"given":"Guozhen","family":"Rong","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6121-588X","authenticated-orcid":true,"given":"Wenjun","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianxin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongjie","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,9,16]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/130914164"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480104441267"},{"key":"atypb3","first-page":"148","author":"Ahn J.","year":"2020","journal-title":"Cham"},{"key":"atypb4","unstructured":"D. C. Arangno,\n                      Hamiltonicity, Pancyclicity, and Cycle Extendability in Graphs\n                      , PhD thesis, Utah State University, 2014."},{"key":"atypb5","first-page":"41","volume":"174","author":"Beasley L.","year":"2005","journal-title":"Congr. Numer."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2006.01.004"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480104441450"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"G. A. Dirac,\n                      Some theorems on abstract graphs\n                      , Proc. Lond. Math. Soc., s3-2 (1952), pp. 69-81.","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02992776"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90154-1"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"M. R. Fellows, D. Meister, F. A. Rosamond, R. Sritharan, and J. A. Telle,\n                      Leaf powers and their properties: Using the trees\n                      , in Algorithms and Computation, ISAAC 2008, S.H. Hong, H. Nagamochi, T. Fukunaga, eds., Lecture Notes in Computer Science 5369, Springer, Berlin, Heidelberg, 2008, pp. 402-413,https:\/\/doi.org\/10.1007\/978-3-540-92182-0_37.","DOI":"10.1007\/978-3-540-92182-0_37"},{"key":"atypb12","unstructured":"A. Gerek,\n                      Hendry's Conjecture on Chordal Graph Subclasses\n                      , PhD thesis, Lehigh University, 2017."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(89)90042-7"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(90)90163-C"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(91)90044-K"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190050314"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00505-8"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/13094551X"},{"key":"atypb19","unstructured":"M. Lafond, B. Seamone, and R. Sherkati,\n                      Further Results on Hendry's Conjecture\n                      , preprint,arXiv:2007.07464[math. co], 2020,https:\/\/arxiv.org\/abs\/2007.07464."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-016-1707-x"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2006.03.030"},{"key":"atypb22","unstructured":"D. B. West,\n                      Introduction to Graph Theory\n                      , Prentice-Hall, Hoboken, NJ, 2000."}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1369920","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:07:20Z","timestamp":1787321240000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1369920"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1369920"],"URL":"https:\/\/doi.org\/10.1137\/20m1369920","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}