Abstract The question whether the Simplex Algorithm admits an efficient pivot rule remains one of most important open questions in discrete optimization. While many natural, deterministic rules are known to yield exponential running times, random-facet was shown have a subexponential time. For long time, Zadeh’s remained prominent candidate for first with We present lower bound construction tha...

Abstract The set‐coloring Ramsey number is defined to be the minimum such that if each edge of complete graph assigned a set colors from , then one contains monochromatic clique size . case usual ‐color number, and was studied by Erdős, Hajnal Rado in 1965, Erdős Szemerédi 1972. first significant results for general were obtained only recently, Conlon, Fox, He, Mubayi, Suk Verstraëte, who showe...