{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T18:16:46Z","timestamp":1791137806513,"version":"4.1.0"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[1998,11]]},"abstract":"<jats:p>\n                    The richest class of t-perfect graphs known so far consists of the graphs with no so-called odd-K. Clearly, these graphs have the special property that they are hereditary t-perfect in the sense that every subgraph is also t-perfect, but they are not the only ones. In this paper we characterize hereditary t-perfect graphs by showing that any non--t-perfect graph contains a non--t-perfect subdivision of K\n                    <jats:sub>4<\/jats:sub>\n                    , called a bad-K\n                    <jats:sub>4<\/jats:sub>\n                    . To prove the result we show which \"weakly 3-connected\" graphs contain no bad-K\n                    <jats:sub>4<\/jats:sub>\n                    ; as a side-product of this we get a polynomial time recognition algorithm.\n                  <\/jats:p>\n                  <jats:p>It should be noted that our result does not characterize t-perfection, as that is not maintained when taking subgraphs but only when taking induced subgraphs.<\/jats:p>","DOI":"10.1137\/s0895480196306361","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"524-545","source":"Crossref","is-referenced-by-count":16,"title":["The Graphs with All Subgraphs T-Perfect"],"prefix":"10.1137","volume":"11","author":[{"given":"A. M. H.","family":"Gerards","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"F. B.","family":"Shepherd","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480190182678"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90160-2"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(79)90062-5"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(73)90167-2"},{"key":"R5","first-page":"83","volume":"16","author":"Fonlupt J.","year":"1982","journal-title":"Ann. Discrete Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0167-5060","issn-type":"print"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(89)90032-4"},{"key":"R7","volume-title":"Graphs and polyhedra. Binary spaces and cutting planes","author":"Gerards A.","year":"1990"},{"key":"R8","unstructured":"A. M. H. Gerards, L. Lov\u00e1sz, A. Schrijver, P. D. Seymour, C.\u2010H. Shih, and K. Truemper,\n                      Regular matroids from graphs\n                      , in preparation."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579262"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(84)90071-2"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5610(95)00034-8"},{"key":"R12","unstructured":"B. Toft,\n                      Problem\n                      10, in Recent Advances in Graph Theory: Proc. Symposium Prague, June 1974, M. Fiedler, ed., Academia, Praha, 1975, pp. 543\u2013544."}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895480196306361","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:02:14Z","timestamp":1787317334000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895480196306361"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,11]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,11]]}},"alternative-id":["10.1137\/S0895480196306361"],"URL":"https:\/\/doi.org\/10.1137\/s0895480196306361","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,11]]}}}