A note on Hedetniemi's conjecture, Stahl's conjecture and the Poljak-Rödl function (Q2278108)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on Hedetniemi's conjecture, Stahl's conjecture and the Poljak-Rödl function |
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A note on Hedetniemi's conjecture, Stahl's conjecture and the Poljak-Rödl function (English)
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9 December 2019
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Summary: We prove that \(\min\{\chi(G),\chi(H)\}-\chi(G\times H)\) can be arbitrarily large, and that if Stahl's conjecture [\textit{S. Stahl}, J. Comb. Theory, Ser. B 20, 185--203 (1976; Zbl 0293.05115)] on the multichromatic number of Kneser graphs holds, then \(\min\{\chi(G),\chi(H)\}/\chi(G\times H)\leq 1/2+\varepsilon\) for large values of \(\min\{\chi(G),\chi(H)\}\).
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