Values of a multifuncoid on atoms ★★

Author(s): Porton

Conjecture   $ L \in \mathrel{\left[ f \right]} \Rightarrow \mathrel{\left[ f \right]} \cap \prod_{i \in \operatorname{dom} \mathfrak{A}} \operatorname{atoms} L_i \neq \emptyset $ for every multifuncoid $ f $ of the form whose elements are atomic posets.

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Oakley sunglasses can successfully secure their sight will very likely be common-sense ★★

Author(s):

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The Borodin-Kostochka Conjecture ★★

Author(s): Borodin; Kostochka

Conjecture   Every graph with maximum degree $ \Delta \geq 9 $ has chromatic number at most $ \max\{\Delta-1, \omega\} $.

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Chromatic number of random lifts of complete graphs ★★

Author(s): Amit

Question   Is the chromatic number of a random lift of $ K_5 $ concentrated on a single value?

Keywords: random lifts, coloring