AbstractWe conjecture that for any fixed r and sufficiently large n, there is a monochromatic Hamiltonian Berge-cycle in every (r−1)-coloring of the edges of Kn(r), the complete r-uniform hypergraph on n vertices. We prove the conjecture for r=3,n⩾5 and its asymptotic version for r=4. For general r we prove weaker forms of the conjecture: there is a Hamiltonian Berge-cycle in ⌊(r−1)/2⌋-colorings of Kn(r) for large n; and a Berge-cycle of order (1−o(1))n in (r−⌊log2r⌋)-colorings of Kn(r). The asymptotic results are obtained with the Regularity Lemma via the existence of monochromatic connected almost perfect matchings in the multicolored shadow graph induced by the coloring of Kn(r)
This thesis contains problems in finding spanning subgraphs in graphs, such as, perfect matchings, t...
AbstractWe say that a k-uniform hypergraph C is an ℓ-cycle if there exists a cyclic ordering of the ...
It is shown that, for >0 and n>n0(), any complete graph K on n vertices whose edges are colored so t...
Here improving on our earlier results we prove that there exists an n0 such that for n ¸ n0, in ever...
Let K(k)n be the complete k-uniform hypergraph, k≥3, and let ℓ be an integer such that 1≤ℓ≤k−1 and k...
We define and study a special type of hypergraph. A σ-hypergraph H = H(n, r, q | σ), where σ is a pa...
A Berge cycle of length $k$ in a hypergraph $\mathcal H$ is a sequence of distinct vertices and hype...
Edge colorings of r -uniform hypergraphs naturally de¯ne a multicolor-ing on the 2-shadow, i.e. on t...
We define and study a special type of hypergraph. A $\sigma$-hypergraph $H= H(n,r,q$ $\mid$ $\sigma$...
Colour the edges of a complete graph with n vertices in such a way that no vertex is on more than k ...
For a graph G, a hypergraph \scrH is a Berge copy of G (or a Berge-G in short) if there is a biject...
Abstract. We say that a k-uniform hypergraph C is an `-cycle if there exists a cyclic ordering of th...
n be the complete k-uniform hypergraph, k ≥ 3, and let ` be an integer such that 1 ≤ ` ≤ k − 1 and...
Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of Kn with n colo...
This thesis contains problems in finding spanning subgraphs in graphs, such as, perfect matchings, t...
This thesis contains problems in finding spanning subgraphs in graphs, such as, perfect matchings, t...
AbstractWe say that a k-uniform hypergraph C is an ℓ-cycle if there exists a cyclic ordering of the ...
It is shown that, for >0 and n>n0(), any complete graph K on n vertices whose edges are colored so t...
Here improving on our earlier results we prove that there exists an n0 such that for n ¸ n0, in ever...
Let K(k)n be the complete k-uniform hypergraph, k≥3, and let ℓ be an integer such that 1≤ℓ≤k−1 and k...
We define and study a special type of hypergraph. A σ-hypergraph H = H(n, r, q | σ), where σ is a pa...
A Berge cycle of length $k$ in a hypergraph $\mathcal H$ is a sequence of distinct vertices and hype...
Edge colorings of r -uniform hypergraphs naturally de¯ne a multicolor-ing on the 2-shadow, i.e. on t...
We define and study a special type of hypergraph. A $\sigma$-hypergraph $H= H(n,r,q$ $\mid$ $\sigma$...
Colour the edges of a complete graph with n vertices in such a way that no vertex is on more than k ...
For a graph G, a hypergraph \scrH is a Berge copy of G (or a Berge-G in short) if there is a biject...
Abstract. We say that a k-uniform hypergraph C is an `-cycle if there exists a cyclic ordering of th...
n be the complete k-uniform hypergraph, k ≥ 3, and let ` be an integer such that 1 ≤ ` ≤ k − 1 and...
Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of Kn with n colo...
This thesis contains problems in finding spanning subgraphs in graphs, such as, perfect matchings, t...
This thesis contains problems in finding spanning subgraphs in graphs, such as, perfect matchings, t...
AbstractWe say that a k-uniform hypergraph C is an ℓ-cycle if there exists a cyclic ordering of the ...
It is shown that, for >0 and n>n0(), any complete graph K on n vertices whose edges are colored so t...