A note on equitable Hamiltonian cycles

被引：0

作者：

Ophelders, Tim ^{[1
]}

Lambers, Roel ^{[2
]}

Spieksma, Frits C. R. ^{[2
]}

Vredeveld, Tjark ^{[3
]}

机构：

[1] Michigan State Univ, Dept Computat Math Sci & Engn, E Lansing, MI 48824 USA

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, Eindhoven, Netherlands

[3] Maastricht Univ, Dept Quantitat Econ, Maastricht, Netherlands

来源：

DISCRETE APPLIED MATHEMATICS | 2021年 / 303卷

基金：

美国国家科学基金会;

关键词：

Equitable Hamiltonian cycle; Colored complete graphs; Polynomial time algorithm; Local search; PERFECT MATCHINGS EXTEND; PATHS;

D O I：

10.1016/j.dam.2020.08.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a complete graph with an even number of vertices, and with each edge colored with one of two colors (say red or blue), an equitable Hamiltonian cycle is a Hamiltonian cycle that can be decomposed into two perfect matchings such that both perfect matchings have the same number of red edges. We show that, for any coloring of the edges, in any complete graph on at least 6 vertices, an equitable Hamiltonian cycle exists. (C) 2020 The Authors. Published by Elsevier B.V.

引用

页码：127 / 136

页数：10

共 50 条

[21] HAMILTONIAN CYCLES IN GRAPHS
LIU, ZH
ZHU, YJ
TIAN, F
ANNALS OF THE NEW YORK ACADEMY OF SCIENCES, 1989, 576 : 367 - 376
[22] Enumerating Hamiltonian Cycles
Pettersson, Ville H.
ELECTRONIC JOURNAL OF COMBINATORICS, 2014, 21 (04):
[23] A REMARK ON HAMILTONIAN CYCLES
VUDINHHOA
MATHEMATISCHE NACHRICHTEN, 1992, 157 : 163 - 168
[24] A note on equitable colorings of forests
Chang, Gerard J.
EUROPEAN JOURNAL OF COMBINATORICS, 2009, 30 (04) : 809 - 812
[25] Note on equitable coloring of graphs
Karthick, T.
AUSTRALASIAN JOURNAL OF COMBINATORICS, 2014, 59 : 251 - 259
[26] On Hamiltonian cycles as optimal p-cycles
Schupke, DA
IEEE COMMUNICATIONS LETTERS, 2005, 9 (04) : 360 - 362
[27] ENUMERATION OF HAMILTONIAN CYCLES ON A THICK GRID CYLINDER - PART II: CONTRACTIBLE HAMILTONIAN CYCLES
Bodroza-Pantic, Olga
Kwong, Harris
Dokic, Jelena
Doroslovacki, Rade
Pantic, Milan
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2022, 16 (01) : 246 - 287
[28] DECOMPOSITION OF THE CARTESIAN SUM OF ONE CYCLE AND THE UNION OF 2 HAMILTONIAN CYCLES INTO HAMILTONIAN CYCLES
AUBERT, J
SCHNEIDER, B
DISCRETE MATHEMATICS, 1982, 38 (01) : 7 - 16
[29] A note on Hamiltonian paths and cycles with prescribed edges in the 3-ary n-cube
Yang, Yuxing
Wang, Shiying
INFORMATION SCIENCES, 2015, 296 : 42 - 45
[30] A Note on Hamiltonian Grids
孙良
数学研究与评论, 1989, (02) : 274 - 276

← 1 2 3 4 5 →