For every fixed r and s, the minimum number of edges in a host hypergraph that forces a monochromatic r-uniform tight path on n vertices under any s-colouring grows only linearly in n.
II , Mathematics of Ramsey Theory, Springer Berlin Heidelberg, Berlin, Heidelberg, 1990, pp
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Size-Ramsey numbers of tight paths
For every fixed r and s, the minimum number of edges in a host hypergraph that forces a monochromatic r-uniform tight path on n vertices under any s-colouring grows only linearly in n.