Name
Abstract | ||
|---|---|---|
Let $${K_n^{(k)}}$$ K n ( k ) be the complete k -uniform hypergraph, $${k\ge3}$$ k 3 , and let ℓ be an integer such that 1 ≤ ℓ ≤ k 1 and k ℓ divides n . An ℓ-overlapping Hamilton cycle in $${K_n^{(k)}}$$ K n ( k ) is a spanning subhypergraph C of $${K_n^{(k)}}$$ K n ( k ) with n /( k ℓ) edges and such that for some cyclic ordering of the vertices each edge of C consists of k consecutive vertices and every pair of consecutive edges in C intersects in precisely ℓ vertices. An edge-coloring of $${K_n^{(k)}}$$ K n ( k ) is ( a , r )-bounded if every subset of a vertices of $${K_n^{(k)}}$$ K n ( k ) is contained in at most r edges of the same color. In this paper, we refine recent results of the first author, Frieze and Ruciński by proving that there is a constant c = c ( k , ℓ) such that every $${(\ell, cn^{k-\ell})}$$ ( ℓ , c n k - ℓ ) -bounded edge-colored $${K_n^{(k)}}$$ K n ( k ) in which no color appears more that cn k -1 times contains a rainbow ℓ-overlapping Hamilton cycle. We also show that there is a constant c = c ( k , ℓ) such that every (ℓ, c n k -ℓ)-bounded edge-colored $${K_n^{(k)}}$$ K n ( k ) contains a properly colored ℓ-overlapping Hamilton cycle. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s00373-013-1391-z | Graphs and Combinatorics |
Keywords | Field | DocType |
Hamiltonian cycle, Rainbow, Uniform hypergraph, 05C38, 05C65, 05C35 | Integer,Combinatorics,Vertex (geometry),Hamiltonian path,Hypergraph,Constraint graph,Rainbow,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
31 | 3 | 1435-5914 |
Citations | PageRank | References |
1 | 0.40 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrzej Dudek | 1 | 114 | 23.10 |
| Michael Ferrara | 2 | 31 | 10.52 |