A FAST ALGORITHM FOR EQUITABLE COLORING

被引：47

作者：

Kierstead, Henry A. ^{[1
]}

Kostochka, Alexandr V. ^{[2
,5
]}

Mydlarz, Marcelo ^{[4
]}

Szemeredi, Endre ^{[3
]}

机构：

[1] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Rutgers State Univ, Dept Comp Sci, Piscataway, NJ 08854 USA

[4] Yahoo Res Latin Amer, Santiago, Chile

[5] Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

COMBINATORICA | 2010年 / 30卷 / 02期

基金：

美国国家科学基金会; 俄罗斯基础研究基金会;

关键词：

BLOW-UP LEMMA; THEOREM; GRAPHS;

D O I：

10.1007/s00493-010-2483-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemeredi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r + 1 colors. We show that this coloring can be obtained in O(rn(2)) time, where n is the number of vertices.

引用

页码：217 / 224

页数：8

共 50 条

[1] A fast algorithm for equitable coloring
Henry A. Kierstead
Alexandr V. Kostochka
Marcelo Mydlarz
Endre Szemerédi
[J]. Combinatorica, 2010, 30 : 217 - 224
[2] A Fast Algorithm for Computing a Nearly Equitable Edge Coloring with Balanced Conditions
Shioura, Akiyoshi
Yagiura, Mutsunori
[J]. COMPUTING AND COMBINATORICS, PROCEEDINGS, 2009, 5609 : 116 - +
[3] A fast algorithm for computing a nearly equitable edge coloring with balanced conditions
Shioura, Akiyoshi
Yagiura, Mutsunori
[J]. Journal of Graph Algorithms and Applications, 2010, 14 (02) : 391 - 407
[4] A DSATUR-based algorithm for the Equitable Coloring Problem
Mendez-Diaz, Isabel
Nasini, Graciela
Severin, Daniel
[J]. COMPUTERS & OPERATIONS RESEARCH, 2015, 57 : 41 - 50
[5] EQUITABLE COLORING
MEYER, W
[J]. AMERICAN MATHEMATICAL MONTHLY, 1973, 80 (08): : 920 - 922
[6] An improved algorithm for the nearly equitable edge-coloring problem
Xie, XZ
Ono, T
Nakano, S
Hirata, T
[J]. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2004, E87A (05): : 1029 - 1033
[7] EQUITABLE COLORING OF TREES
CHEN, BL
LIH, KW
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1994, 61 (01) : 83 - 87
[8] A FAST ALGORITHM FOR COLORING MEYNIEL GRAPHS
HERTZ, A
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1990, 50 (02) : 231 - 240
[9] Equitable coloring of hypergraphs
Furmanczyk, Hanna
Obszarski, Pawel
[J]. DISCRETE APPLIED MATHEMATICS, 2019, 261 : 186 - 192
[10] Incidence coloring of Mycielskians with fast algorithm
Bi, Huimin
Zhang, Xin
[J]. THEORETICAL COMPUTER SCIENCE, 2021, 878 : 1 - 10

← 1 2 3 4 5 →