The Ramsey number of generalized loose paths in uniform Hypergrpahs

@inproceedings{Peng2013TheRN,
  title={The Ramsey number of generalized loose paths in uniform Hypergrpahs},
  author={Xing Peng},
  year={2013}
}
Let H = (V, E) be an r-uniform hypergraph. For each 1 ≤ s ≤ r − 1, an spath P n in H of length n is a sequence of distinct vertices v1, v2, . . . , vs+n(r−s) such that {v1+i(r−s), . . . , vs+(i+1)(r−s)} ∈ E(H) for each 0 ≤ i ≤ n − 1. Recently, the Ramsey number of 1-paths and 1-cycles in uniform hypergraphs attracted a lot of attention. The asymptotic value of R(P n ,P 3,1 n ) was first determined. The exact values of R(P 3 ,P r,1 3 ) and R(P r,1 4 ,P r,1 4 ) are known; for n ≥ m ≥ 1, R(P 3,1 n… CONTINUE READING

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