منابع مشابه
Long Monochromatic Berge Cycles in Colored 4-Uniform Hypergraphs
Here we prove that for n ≥ 140, in every 3-coloring of the edges of K (4) n there is a monochromatic Berge cycle of length at least n− 10. This result sharpens an asymptotic result obtained earlier. Another result is that for n ≥ 15, in every 2-coloring of the edges of K n there is a 3-tight Berge cycle of length at least n− 10.
متن کاملMonochromatic Hamiltonian Berge-cycles in colored complete uniform hypergraphs
We conjecture that for any fixed r and sufficiently large n, there is a monochromatic Hamiltonian Bergecycle in every (r − 1)-coloring of the edges of K n , 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...
متن کاملDecompositions of complete uniform hypergraphs into Hamilton Berge cycles
In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if n divides ( n k ) , then the complete k-uniform hypergraph on n vertices has a decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an alternating sequence v1, e1, v2, . . . , vn, en of distinct vertices vi and distinct edges ei so that each ei contains vi and vi+1. So the divisibility condition is clearly nec...
متن کاملMonochromatic Hamiltonian 3-tight Berge cycles in 2-colored 4-uniform hypergraphs
Here improving on our earlier results we prove that there exists an n0 such that for n ≥ n0, in every 2-coloring of the edges of K n there is a monochromatic Hamiltonian 3-tight Berge cycle. This proves the c = 2, t = 3, r = 4 special case of a conjecture from [5].
متن کاملMonochromatic Hamiltonian t-tight Berge-cycles in hypergraphs
In any r-uniform hypergraph H for 2 ≤ t ≤ r we define an runiform t-tight Berge-cycle of length , denoted by C , as a sequence of distinct vertices v1, v2, . . . , v , such that for each set (vi , vi+1, . . . ,vi+t−1 ) of t consecutive vertices on the cycle, there is an edge Ei of H that contains these t vertices and the edges Ei are all distinct for i, 1 ≤ i ≤ , where + j ≡ j. For t = 2 we get...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/9346