Non-monochromatic and conflict-free colorings on tree spaces and planar network spaces

Boris Aronov; Mark de Berg; Aleksandar Markovic; Gerhard Woeginger

doi:10.1007/s00453-019-00639-9

Non-monochromatic and conflict-free colorings on tree spaces and planar network spaces

Boris Aronov
, Mark de Berg
, Aleksandar Markovic (Corresponding author)
, Gerhard Woeginger

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

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Abstract

It is well known that any set of n intervals in R¹ admits a non-monochromatic coloring with two colors and a conflict-free coloring with three colors. We investigate generalizations of this result to colorings of objects in more complex 1-dimensional spaces, namely so-called tree spaces and planar network spaces.

Original language	English
Pages (from-to)	1081-1100
Number of pages	20
Journal	Algorithmica
Volume	82
Issue number	5
Early online date	31 Oct 2019
DOIs	https://doi.org/10.1007/s00453-019-00639-9
Publication status	Published - 1 May 2020

Funding

Bonfils-Stanton Foundation Acronym: BSF Funding numbers: 2014/170

Funders	Funder number
National Science Foundation	CCF-11-17336, CCF-12-18791, CCF-15-40656
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	024.002.003

Keywords

Conflict-free coloring
Non-monochromatic coloring
Planar networks
Tree

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10.1007/s00453-019-00639-9

publishers versionFinal published version, 559 KBLicence: CC BY

Cite this

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abstract = "It is well known that any set of n intervals in R1 admits a non-monochromatic coloring with two colors and a conflict-free coloring with three colors. We investigate generalizations of this result to colorings of objects in more complex 1-dimensional spaces, namely so-called tree spaces and planar network spaces.",

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AU - de Berg, Mark

AU - Markovic, Aleksandar

AU - Woeginger, Gerhard

PY - 2020/5/1

Y1 - 2020/5/1

N2 - It is well known that any set of n intervals in R1 admits a non-monochromatic coloring with two colors and a conflict-free coloring with three colors. We investigate generalizations of this result to colorings of objects in more complex 1-dimensional spaces, namely so-called tree spaces and planar network spaces.

AB - It is well known that any set of n intervals in R1 admits a non-monochromatic coloring with two colors and a conflict-free coloring with three colors. We investigate generalizations of this result to colorings of objects in more complex 1-dimensional spaces, namely so-called tree spaces and planar network spaces.

KW - Conflict-free coloring

KW - Non-monochromatic coloring

KW - Planar networks

KW - Tree

UR - https://www.scopus.com/pages/publications/85074731029

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DO - 10.1007/s00453-019-00639-9

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Non-monochromatic and conflict-free colorings on tree spaces and planar network spaces

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Keywords

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