Inner reloid through the lattice Gamma ★★

Author(s): Porton

Conjecture   $ (\mathsf{RLD})_{\operatorname{in}} f = \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $ for every funcoid $ f $.

Counter-example: $ (\mathsf{RLD})_{\operatorname{in}} f \sqsubset \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $ for the funcoid $ f = (=)|_\mathbb{R} $ is proved in this online article.

Keywords: filters; funcoids; inner reloid; reloids

Chromatic Number of Common Graphs ★★

Author(s): Hatami; Hladký; Kráľ; Norine; Razborov

Question   Do common graphs have bounded chromatic number?

Keywords: common graph