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On multicolor Ramsey numbers of triple system paths of length 3
Let be a 3-uniform hypergraph. The multicolor Ramsey number is the smallest integer such that every coloring of with colors has a monochromatic copy of . Let
be the loose 3-uniform path with 3 edges and
denote the messy 3-uniform path with 3 edges; that is, let and . In this note we
prove and for
sufficiently large. The former result improves on the bound , which was recently established by {\L}uczak and Polcyn.Comment: 18 pages, 3 figure