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- W2766457447 abstract "A conjecture of Gyárfás and Sárközy says that in every $2$-coloring of the edges of the complete $k$-uniform hypergraph $mathcal{K}_n^k$, there are two disjoint monochromatic loose paths of distinct colors such that they cover all but at most $k-2$ vertices. Recently, the authors affirmed the conjecture. In the note we show that for every $2$-coloring of $mathcal{K}_n^k$, one can find two monochromatic paths of distinct colors to cover all vertices of $mathcal{K}_n^k$ such that they share at most $k-2$ vertices. Omidi and Shahsiah conjectured that $R(mathcal{P}_t^k,mathcal{P}_t^k) =t(k-1)+lfloor frac{t+1}{2}rfloor$ holds for $kge 3$ and they affirmed the conjecture for $k=3$ or $kge 8$. We show that if the conjecture is true, then $k-2$ is best possible for our result." @default.
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- W2766457447 date "2017-10-20" @default.
- W2766457447 modified "2023-09-23" @default.
- W2766457447 title "Cover $k$-Uniform Hypergraphs by Monochromatic Loose Paths" @default.
- W2766457447 doi "https://doi.org/10.37236/6936" @default.
- W2766457447 hasPublicationYear "2017" @default.
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