Geodesic
Chromatic Ramsey numbers of generalised Mycielski graphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 4, pp. 1327-1339

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We revisit the Burr-Erdős-Lovász conjecture on chromatic Ramsey numbers. We show that it admits a proof based on the ϑ parameter in addition to the proof of Xuding Zhu based on the fractional chromatic number. However, there are no proofs based on topological lower bounds on chromatic numbers, because the chromatic Ramsey numbers of generalised Mycielski graphs are too large. We show that the 4-chromatic generalised Mycielski graphs other than K_4 all have chromatic Ramsey number 14, and that the n-chromatic generalised Mycielski graphs all have chromatic Ramsey number at least 2^n//4.
Keywords: chromatic Ramsey numbers, fractional chromatic numbers, Lovász $\vartheta$ parameter, box complexes, generalised Mycielski graphs 
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     author = {Tardif, Claude},
     title = {Chromatic {Ramsey} numbers of generalised {Mycielski} graphs},
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Tardif, Claude. Chromatic Ramsey numbers of generalised Mycielski graphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 4, pp. 1327-1339. http://geodesic.mathdoc.fr/item/DMGT_2024_44_4_a5/