# Monochromatic loose paths in multicolored k-uniform cliques

@article{Dudek2019MonochromaticLP, title={Monochromatic loose paths in multicolored k-uniform cliques}, author={Andrzej Dudek and Andrzej Rucinski}, journal={Discret. Math. Theor. Comput. Sci.}, year={2019}, volume={21} }

For positive integers $k$ and $\ell$, a $k$-uniform hypergraph is called a \emph{loose path of length~$\ell$}, and denoted by $P_\ell^{(k)}$, if it consists of $\ell $ edges $e_1,\dots,e_\ell$ such that $|e_i\cap e_j|=1$ if $|i-j|=1$ and $e_i\cap e_j=\emptyset$ if $|i-j|\ge2$. In other words, each pair of consecutive edges intersects on a single vertex, while all other pairs are disjoint. Let $R(P_\ell^{(k)};r)$ be the minimum integer $n$ such that every $r$-edge-coloring of the complete $k…

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