The Boolean Rainbow Ramsey Number of Antichains, Boolean Posets, and Chains

2019/09/25 by Chen, Hong-Bin, Cheng, Yen-Jen, Li, Wei-Tian +1 · 1 citation
#06A07 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.11370

Abstract

Motivated by the paper of Axenovich and Walzer [2], we study the Ramsey-type problems on the Boolean lattices. Given posets P and Q, we look for the smallest Boolean lattice B_N such that any coloring on elements of B_N must contain a monochromatic P or a rainbow Q. This number N is called the Boolean rainbow Ramsey number of P and Q in the paper. Particularly, we determine the exact values of the Boolean rainbow Ramsey number for P and Q being the antichains, the Boolean posets, or the chains. From these results, we also give some general upper and lower bounds of the Boolean rainbow Ramsey number for general P and Q in terms of the poset parameters.

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• Constrained Ramsey numbers for rainbow P₅

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