Equitable colorings of hypergraphs with few edges

被引：6
|
作者：
Akhmejanova, Margarita B. [1 ]
Shabanov, Dmitry A. [1 ,2 ,3 ]
机构：
[1] Moscow Inst Phys & Technol, Lab Adv Combinator & Network Applicat, Inst Skiy 9, Dolgoprudnyi 141700, Moscow Region, Russia
[2] Lomonosov Moscow State Univ, Fac Mech & Math, Dept Probabil Theory, Leninskie Gory 1, Moscow 119991, Russia
[3] Natl Res Univ Higher Sch Econ HSE, Fac Comp Sci, Myasnitskaya Str 20, Moscow 101000, Russia
来源：
DISCRETE APPLIED MATHEMATICS | 2020年 / 276卷
关键词：
Uniform hypergraphs; Proper colorings; Equitable colorings; Pluhar's criterion; CHROMATIC NUMBER; THEOREM; GRAPHS;
D O I：
10.1016/j.dam.2019.03.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper deals with an extremal problem concerning equitable colorings of uniform hypergraph. Recall that a vertex coloring of a hypergraph H is called proper if there are no monochromatic edges under this coloring. A hypergraph is said to be equitably r-colorable if there is a proper coloring with r colors such that the sizes of any two color classes differ by at most one. In the present paper we prove that if the number of edges vertical bar E(H)vertical bar <= 0.01 (n/ln n)(r-)(1/r) rn-1 then the hypergraph H is equitably r-colorable provided r < (5)root ln n. (C) 2019 Elsevier B.V. All rights reserved.
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页码：2 / 12
页数：11
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