A note on equitable Hamiltonian cycles

T. Ophelders; R. Lambers; F.C.R. Spieksma; T. Vredeveld

doi:10.1016/j.dam.2020.08.023

A note on equitable Hamiltonian cycles

T. Ophelders, R. Lambers, F.C.R. Spieksma, T. Vredeveld^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Pages (from-to)	127-136
Number of pages	10
Journal	Discrete Applied Mathematics
Volume	303
DOIs	https://doi.org/10.1016/j.dam.2020.08.023
Publication status	Published - 15 Nov 2021

Keywords

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

Access to Document

10.1016/j.dam.2020.08.023Licence: CC BY

Cite this

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abstract = "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.",

keywords = "Equitable Hamiltonian cycle, Colored complete graphs, Polynomial time algorithm, Local search, PERFECT MATCHINGS EXTEND, PATHS",

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AU - Vredeveld, T.

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KW - Equitable Hamiltonian cycle

KW - Colored complete graphs

KW - Polynomial time algorithm

KW - Local search

KW - PERFECT MATCHINGS EXTEND

KW - PATHS

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DO - 10.1016/j.dam.2020.08.023

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