On irredundance coloring and irredundance compelling coloring of graphs

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Publication Details

Author list: Kalarkop D.A.; Henning M.A.; Hamid I.S.; Kaemawichanurat P.

Publisher: Elsevier

Publication year: 2025

Volume number: 369

Start page: 149

End page: 161

Number of pages: 13

ISSN: 0166-218X

eISSN: 1872-6771

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-105001163500&doi=10.1016%2fj.dam.2025.03.025&partnerID=40&md5=a7666d3d4d4226354775333a5f173a07

Languages: English-Great Britain (EN-GB)

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Abstract

An irredundance coloring of a graph G is a proper coloring admitting a maximal irredundant set all of whose vertices receive different colors. The minimum number of colors required for an irredundance coloring of G is called the irredundance chromatic number of G, and is denoted by χi(G). An irredundance compelling coloring of G is a proper coloring of G in which every rainbow committee (a set consisting of one vertex of each color) is an irredundant set of G. The maximum number of colors required for an irredundance compelling coloring of G is called the irredundance compelling chromatic number of G, and is denoted by χirc(G). We make a detailed study of χi(G), χirc(G), derive bounds on these parameters and characterize extremal graphs attaining the bounds. © 2025 The Author(s)

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