{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:04:55Z","timestamp":1777421095602,"version":"3.51.4"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n\t\t\t\t<jats:p>Harary [10, p. 7] claims that Veblen [20, p. 2] first suggested to formalize simple graphs using simplicial complexes. We have developed basic terminology for simple graphs as at most 1-dimensional complexes.<\/jats:p>\n\t\t\t\t<jats:p>We formalize this new setting and then reprove Mycielski\u2019s [12] construction resulting in a triangle-free graph with arbitrarily large chromatic number. A different formalization of similar material is in [15].<\/jats:p>","DOI":"10.2478\/v10037-012-0019-8","type":"journal-article","created":{"date-parts":[[2013,2,4]],"date-time":"2013-02-04T17:14:25Z","timestamp":1359998065000},"page":"161-174","source":"Crossref","is-referenced-by-count":2,"title":["Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph"],"prefix":"10.2478","volume":"20","author":[{"given":"Piotr","family":"Rudnicki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lorna","family":"Stewart","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/20\/2\/article-p161.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2012.20.issue-2\/v10037-012-0019-8\/v10037-012-0019-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:28:37Z","timestamp":1590852517000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-012-0019-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,1]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/v10037-012-0019-8","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2012,12,1]]}}}