{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T15:58:48Z","timestamp":1648828728253},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"03n04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:p>A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G containing these k vertices in the specified order. It is k-ordered Hamiltonian if, in addition, the required cycle is Hamiltonian. The question of the existence of an infinite class of 3-regular 4-ordered Hamiltonian graphs was posed in 1997 by Ng and Schultz.<jats:sup>13<\/jats:sup>At the time, the only known examples were K<jats:sub>4<\/jats:sub>and K<jats:sub>3,3<\/jats:sub>. Some progress was made in 2008 by M\u00e9sz\u00e1ros,<jats:sup>12<\/jats:sup>when the Peterson graph was found to be 4-ordered and the Heawood graph was proved to be 4-ordered Hamiltonian; moreover, an infinite class of 3-regular 4-ordered graphs was found. In 2010 a subclass of generalized Petersen graphs was shown to be 4-ordered by Hsu et al.,<jats:sup>10<\/jats:sup>with an infinite subset of this subclass being 4-ordered Hamiltonian, thus answering the open question. In this paper we find another infinite class of 3-regular 4-ordered Hamiltonian graphs, part of a subclass of the chordal ring graphs. In addition, we classify precisely which of these graphs are 4-ordered Hamiltonian.<\/jats:p>","DOI":"10.1142\/s0219265910002787","type":"journal-article","created":{"date-parts":[[2011,4,13]],"date-time":"2011-04-13T01:49:04Z","timestamp":1302659344000},"page":"157-174","source":"Crossref","is-referenced-by-count":0,"title":["4-ORDERED HAMILTONICITY FOR SOME CHORDAL RING GRAPHS"],"prefix":"10.1142","volume":"11","author":[{"given":"DAVID","family":"SHERMAN","sequence":"first","affiliation":[{"name":"University of Michigan, Ann Arbor, MI 48109, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MING","family":"TSAI","sequence":"additional","affiliation":[{"name":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 30010, ROC"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHENG-KUAN","family":"LIN","sequence":"additional","affiliation":[{"name":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 30010, ROC"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L\u00c1SZL\u00d3","family":"LIPT\u00c1K","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EDDIE","family":"CHENG","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIMMY J. M.","family":"TAN","sequence":"additional","affiliation":[{"name":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 30010, ROC"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LIH-HSING","family":"HSU","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Information Engineering, Providence University, Taichung, Taiwan 43301, ROC"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.12.016"},{"key":"rf2","first-page":"98","volume":"56","author":"Behzad M.","journal-title":"Bulletin of the Institute of Combinatorics and its Applications"},{"key":"rf3","first-page":"245","volume":"70","author":"Chen G.","journal-title":"Ars Combinatoria"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(02)00507-0"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00458-1"},{"key":"rf6","doi-asserted-by":"crossref","first-page":"R11","DOI":"10.37236\/1704","volume":"10","author":"Faundree J. 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