Equitable Colorings of Hypergraphs with r Colors
نویسندگان
چکیده
The paper deals with a problem concerning equitable vertex colorings of uniform hypergraphs, i.e., under which there are no monochromatic edges and simultaneously all the color classes have almost same cardinalities. We obtain new bound on edge number an n-uniform hypergraph that guarantees existence coloring r colors for this hypergraph.
منابع مشابه
Equitable two-colorings of uniform hypergraphs
An equitable two-coloring of a hypergraph H = (V, E) is a proper vertex two-coloring such that the cardinalities of color classes differ by at most one. In connection with property B problem Radhakrishnan and Srinivasan proved that if H is a k-uniform hypergraph with maximum vertex degree ∆(H) satisfying ∆(H) c 2 k−1 √ k ln k (1) for some absolute constant c > 0, then H is 2-colorable. By using...
متن کاملEquitable colorings of non-uniform simple hypergraphs
The paper is devoted to the combinatorial problem concerning equitable colorings of non-uniform simple hypergraphs. Let H = (V,E) be a hypergraph, a coloring with r colors of its vertex set V is called equitable if it is proper (i.e. none of the edges is monochromatic) and the cardinalities of the color classes differ by at most one. We show that if H is a simple hypergraph with minimum edge-ca...
متن کاملColorings of hypergraphs with large number of colors
The paper deals with the well-known problem of Erdős and Hajnal concerning colorings of uniform hypergraphs and some related questions. Let m(n, r) denote the minimum possible number of edges in an n-uniform non-r-colorable hypergraph. We show that for r > n, c1 n lnn m(n, r) rn C1 n lnn, where c1, C1 > 0 are some absolute constants.
متن کاملA note on r-equitable k-colorings of trees
A graph G = (V,E) is r-equitably k-colorable if there exists a partition of V into k independent sets V1, V2, · · · , Vk such that | |Vi| − |Vj | | ≤ r for all i, j ∈ {1, 2, · · · , k}. In this note, we show that if two trees T1 and T2 of order at least two are r-equitably k-colorable for r ≥ 1 and k ≥ 3, then all trees obtained by adding an arbitrary edge between T1 and T2 are also r-equitably...
متن کاملHypergraphs with many Kneser colorings
For fixed positive integers r, k and ` with 1 ≤ ` < r and an r-uniform hypergraph H, let κ(H, k, `) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least ` elements. Consider the function KC(n, r, k, `) = maxH∈Hn κ(H, k, `), where the maximum runs over the family Hn of all r-uniform hypergraphs on n vertices. In...
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: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-05823-x