Path-path Ramsey-type numbers for the complete bipartite graph

@article{Faudree1975PathpathRN,
  title={Path-path Ramsey-type numbers for the complete bipartite graph},
  author={R. Faudree and R. Schelp},
  journal={Journal of Combinatorial Theory, Series B},
  year={1975},
  volume={19},
  pages={161-173}
}
Abstract For a fixed pair of integers r, s ≥ 2, all positive integers m and n are determined which have the property that if the edges of Km,n (a complete bipartite graph with parts n and m) are colored with two colors, then there will always exist a path with r vertices in the first color or a path with s vertices in the second color. 
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