2018
DOI: 10.1016/j.dam.2017.08.008
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The b-chromatic number and related topics—A survey

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Cited by 21 publications
(13 citation statements)
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“…Later, Cabello and Jakovac (2011) proved that for every d-regular graph with at least 2d 3 vertices χ b (G) = ∆ + 1. A detailed review of the literature related to the b-chromatic number can be found in Jakovac and Peterin (2018).…”
Section: Introduction 1basic Notation and Problem Definitionmentioning
confidence: 99%
“…Later, Cabello and Jakovac (2011) proved that for every d-regular graph with at least 2d 3 vertices χ b (G) = ∆ + 1. A detailed review of the literature related to the b-chromatic number can be found in Jakovac and Peterin (2018).…”
Section: Introduction 1basic Notation and Problem Definitionmentioning
confidence: 99%
“…Also by a color dominating vertex u of G we mean the vertex u has at least one neighbor in each color class of the color-dominating coloring of G. Denote by b(G) the maximum number of colors used in any color-dominating coloring of G. The b-chromatic number has been widely studied in graph theory [2,3,4,7,8,10,11,12,13]. For a survey on b-chromatic number, we refer to [9]. In this paper we call a graph G b-monotone if for each induced subgraph H of G we have b(H) ≤ b(G).…”
Section: Introductionmentioning
confidence: 99%
“…The b-chromatic number b(G) is the largest integer k such that G admits a b-coloring with k colors. Since this parameter has been introduced by R. W. Irving and D. F. Manlove [6], it aroused the interest of many researchers as we can see in [5], [2] and [3] and, more recently, in [7].…”
Section: Introductionmentioning
confidence: 99%