On the complexity of rainbow coloring problems

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F18%3A00106820" target="_blank" >RIV/00216224:14330/18:00106820 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1016/j.dam.2016.10.021" target="_blank" >http://dx.doi.org/10.1016/j.dam.2016.10.021</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.dam.2016.10.021" target="_blank" >10.1016/j.dam.2016.10.021</a>

Result language

angličtina

Original language name

On the complexity of rainbow coloring problems

Original language description

An edge-colored graph is said to be rainbow connected if between each pair of vertices there exists a path which uses each color at most once. The rainbow connection number, denoted by , is the minimum number of colors needed to make rainbow connected. Along with its variants, which consider vertex colorings and/or so-called strong colorings, the rainbow connection number has been studied from both the algorithmic and graph-theoretic points of view. In this paper we present a range of new results on the computational complexity of computing the four major variants of the rainbow connection number. In particular, we prove that the Strong Rainbow Vertex Coloring problem is -complete even on graphs of diameter , and also when the number of colors is restricted to . On the other hand, we show that if the number of colors is fixed then all of the considered problems can be solved in linear time on graphs of bounded treewidth. Moreover, we provide a linear-time algorithm which decides whether it is possible to obtain a rainbow coloring by saving a fixed number of colors from a trivial upper bound. Finally, we give a linear-time algorithm for computing the exact rainbow connection numbers for three variants of the problem on graphs of bounded vertex cover number.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Discrete Applied Mathematics

ISSN

0166-218X

e-ISSN

—

Volume of the periodical

246

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

11

Pages from-to

38-48

UT code for WoS article

000437996700005

EID of the result in the Scopus database

2-s2.0-85006790245