Generalised Mycielski graphs and the Borsuk–Ulam theorem

Tobias Müller*, Matej Stehlik

*Corresponding author voor dit werk

OnderzoeksoutputAcademicpeer review

5 Citaten (Scopus)
142 Downloads (Pure)

Samenvatting

Stiebitz determined the chromatic number of generalised Mycielski graphs using the topological method of Lovász, which invokes the Borsuk–Ulam theorem. Van Ngoc and Tuza used elementary combinatorial arguments to prove Stiebitz's theorem for 4-chromatic generalised Mycielski graphs, and asked if there is also an elementary combinatorial proof for higher chromatic number. We answer their question by showing that Stiebitz's theorem can be deduced from a version of Fan's combinatorial lemma. Our proof uses topological terminology, but is otherwise completely discrete and could be rewritten to avoid topology altogether. However, doing so would be somewhat artificial, because we also show that Stiebitz's theorem is equivalent to the Borsuk–Ulam theorem.
Originele taal-2English
Pagina's (van-tot)1-8
Aantal pagina's7
TijdschriftElectronic Journal of Combinatorics
Volume26
Nummer van het tijdschrift4
DOI's
StatusPublished - 2019

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