{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:39Z","timestamp":1753893819655,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Stiebitz determined the chromatic number of generalised\u00a0Mycielski graphs using the topological method of Lov\u00e1sz,\u00a0which invokes the Borsuk\u2013Ulam theorem. Van Ngoc and Tuza\u00a0used elementary combinatorial arguments to prove Stiebitz's\u00a0theorem for 4-chromatic generalised Mycielski graphs, and\u00a0asked if there is also an elementary combinatorial proof for\u00a0higher chromatic number. We answer their question by showing\u00a0that Stiebitz's theorem can be deduced from a version of Fan's\u00a0combinatorial lemma. Our proof uses topological terminology,\u00a0but is otherwise completely discrete and could be rewritten to\u00a0avoid topology altogether. However, doing so would be somewhat\u00a0artificial, because we also show that Stiebitz's theorem is\u00a0equivalent to the Borsuk\u2013Ulam theorem.<\/jats:p>","DOI":"10.37236\/8462","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:04:48Z","timestamp":1578636288000},"source":"Crossref","is-referenced-by-count":2,"title":["Generalised Mycielski Graphs and the Borsuk\u2013Ulam Theorem"],"prefix":"10.37236","volume":"26","author":[{"given":"Tobias","family":"M\u00fcller","sequence":"first","affiliation":[]},{"given":"Mat\u011bj","family":"Stehl\u00edk","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,10,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p8\/7933","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p8\/7933","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:02:39Z","timestamp":1579233759000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/8462","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,10,11]]},"article-number":"P4.8"}}