{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T12:40:12Z","timestamp":1780663212580,"version":"3.54.1"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":5217,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1994,6]]},"abstract":"<jats:p>It is proved that any plane graph may be represented by a triangle contact system, that is a collection of triangular disks which are disjoint except at contact points, each contact point being a node of exactly one triangle. Representations using contacts of T-or Y-shaped objects follow. Moreover, there is a one-to-one mapping between all the triangular contact representations of a maximal plane graph and all its partitions into three Schnyder trees.<\/jats:p>","DOI":"10.1017\/s0963548300001139","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:17:11Z","timestamp":1221218231000},"page":"233-246","source":"Crossref","is-referenced-by-count":69,"title":["On Triangle Contact Graphs"],"prefix":"10.1017","volume":"3","author":[{"given":"Hubert","family":"de Fraysseix","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrice Ossona","family":"de Mendez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Rosenstiehl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300001139_ref001","first-page":"445","article-title":"On convex polyhedra in Lobacevskii spaces","volume":"81","author":"Andreev","year":"1970","journal-title":"Mat. Sb."},{"key":"S0963548300001139_ref010","unstructured":"[10] Tamassia R. and Tollis I. G. (1989) Tessellation representation of planar graphs. In: Proc. Twenty-Seventh Annual Allerton Conference on Communication, Control, and Computing 48\u201357."},{"key":"S0963548300001139_ref004","unstructured":"[4] de Fraysseix H. , de Mendez P. O. and Pach J. (submitted) A streamlined depth-first search algorithm revisited."},{"key":"S0963548300001139_ref003","unstructured":"[3] de Fraysseix H. and de Mendez P. O. (In preparation) On tree decompositions and angle marking of planar graphs."},{"key":"S0963548300001139_ref007","unstructured":"[7] Mohar B. (To appear) Circle packings of maps in polynomial time."},{"key":"S0963548300001139_ref002","volume-title":"Algorithms for drawing planar graphs: an annotated bibliography","author":"Di Battista","year":"1989"},{"key":"S0963548300001139_ref005","article-title":"Representation of planar graphs by segments","author":"de Fraysseix","year":"1993","journal-title":"Intuitive Geometry"},{"key":"S0963548300001139_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02122694"},{"key":"S0963548300001139_ref009","unstructured":"[9] Schnyder W. (1990) Embedding planar graphs on the grid. In: Proc. ACM-SIAM Symp. on Discrete Algorithms 138\u2013148."},{"key":"S0963548300001139_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187706"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300001139","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T03:52:04Z","timestamp":1557892324000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300001139\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,6]]}},"alternative-id":["S0963548300001139"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300001139","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,6]]}}}