Abstract
A k-graph system H = {Hi}i∈[m] is a family of not necessarily distinct k-graphs on the same n-vertex set V , and a k-graph H on V is said to be H-transversal provided that there exists an injection varp : E(H) \rightarrow [m] such that e ∊ E(H\varphi(e)) for all e ∊ E(H). We show that given k ≥ 3, gamm > 0, sufficiently large n, and an n-vertex k-graph system H = {Hi}i∈[n], if deltk-1(Hi) ≥ (1/2 + gamm)n for each i ∊ [n], then there exists an H-transversal tight Hamilton cycle. This extends the result of Rödl, Ruciński, and Szemerédi [Combinatorica, 28 (2008), pp. 229–260] on single k-graphs.
Original language | English |
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Pages (from-to) | 55-74 |
Number of pages | 20 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 39 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2025 |
Keywords
- Hamilton cycle
- k-graph system
- transversal
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Cheng, Y., Han, J., Wang, B., Wang, G., & Yang, D. (2025). TRANSVERSAL HAMILTON CYCLE IN HYPERGRAPH SYSTEMS. SIAM Journal on Discrete Mathematics, 39(1), 55-74. https://doi.org/10.1137/23M1602425