Anti-Ramsey number of matchings in r-partite r-uniform hypergraphs
نویسندگان
چکیده
An edge-colored hypergraph is rainbow if all of its edges have different colors. Given two hypergraphs H and G , the anti-Ramsey number a r ( ) in maximum colors coloring so that there does not exist copy . Li et al. determined k -matchings complete bipartite graphs. Jin Zang showed uniqueness extremal coloring. In this paper, as generalization these results, we determine K n 1 … M -partite -uniform show Also, − 2 unique for Turán e x = + which gives multi-partite version result Özkahya Young's conjecture.
منابع مشابه
Coverings and matchings in r-partite hypergraphs
Ryser’s conjecture postulates that, for r-partite hypergraphs, τ ≤ (r − 1)ν where τ is the covering number of the hypergraph and ν is the matching number. Although this conjecture has been open since the 1960s, researchers have resolved it for special cases such as for intersecting hypergraphs where r ≤ 5. In this paper, we prove several results pertaining to matchings and coverings in r-partit...
متن کاملAnti-Ramsey number of matchings in hypergraphs
A k-matching in a hypergraph is a set of k edges such that no two of these edges intersect. The anti-Ramsey number of a k-matching in a complete s-uniform hypergraph H on n vertices, denoted by ar(n, s, k), is the smallest integer c such that in any coloring of the edges of H with exactly c colors, there is a k-matching whose edges have distinct colors. The Turán number, denoted by ex(n, s, k),...
متن کاملGeneralized Ramsey theorems for r-uniform hypergraphs
We show that several known Ramsey number inequalities can be extended to the setting of r-uniform hypergraphs. In particular, we extend Burr’s results on tree-star Ramsey numbers, providing exact evaluations for certain hypergraph Ramsey numbers. Then we turn our attention to proving a general multicolor hypergraph Ramsey number inequality from which generalizations of results due to Chvátal an...
متن کاملRainbow Matchings in r-Partite r-Graphs
Given a collection of matchings M = (M1,M2, . . . ,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be s-rainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ : M → [q] such that e ∈ Mφ(e) for all e ∈ M , and |Im(φ)| > s. Let f(r, s, t) be the maximal k for which ...
متن کاملPerfect matchings in r-partite r-graphs
Let H be an r-partite r-graph, all of whose sides have the same size n. Suppose that there exist two sides of H , each satisfying the following condition: the degree of each legal r−1-tuple contained in the complement of this side is strictly larger than n 2 . We prove that under this condition H must have a perfect matching. This answers a question of Kühn and Osthus.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2022
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2021.112782