# Bounds for the b-Chromatic Number of Subgraphs and Edge-Deleted Subgraphs

• Volume: 36, Issue: 4, page 959-976
• ISSN: 2083-5892

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## Abstract

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A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we obtain bounds for the b- chromatic number of induced subgraphs in terms of the b-chromatic number of the original graph. This turns out to be a generalization of the result due to R. Balakrishnan et al. [Bounds for the b-chromatic number of G−v, Discrete Appl. Math. 161 (2013) 1173-1179]. Also we show that for any connected graph G and any e ∈ E(G), b(G - e) ≤ b(G) + [...] -2. Further, we determine all graphs which attain the upper bound. Finally, we conclude by finding bound for the b-chromatic number of any subgraph.

## How to cite

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P. Francis, and S. Francis Raj. "Bounds for the b-Chromatic Number of Subgraphs and Edge-Deleted Subgraphs." Discussiones Mathematicae Graph Theory 36.4 (2016): 959-976. <http://eudml.org/doc/287091>.

@article{P2016,
abstract = {A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we obtain bounds for the b- chromatic number of induced subgraphs in terms of the b-chromatic number of the original graph. This turns out to be a generalization of the result due to R. Balakrishnan et al. [Bounds for the b-chromatic number of G−v, Discrete Appl. Math. 161 (2013) 1173-1179]. Also we show that for any connected graph G and any e ∈ E(G), b(G - e) ≤ b(G) + [...] -2. Further, we determine all graphs which attain the upper bound. Finally, we conclude by finding bound for the b-chromatic number of any subgraph.},
author = {P. Francis, S. Francis Raj},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {b-coloring; b-chromatic number; -coloring; -chromatic number},
language = {eng},
number = {4},
pages = {959-976},
title = {Bounds for the b-Chromatic Number of Subgraphs and Edge-Deleted Subgraphs},
url = {http://eudml.org/doc/287091},
volume = {36},
year = {2016},
}

TY - JOUR
AU - P. Francis
AU - S. Francis Raj
TI - Bounds for the b-Chromatic Number of Subgraphs and Edge-Deleted Subgraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 4
SP - 959
EP - 976
AB - A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we obtain bounds for the b- chromatic number of induced subgraphs in terms of the b-chromatic number of the original graph. This turns out to be a generalization of the result due to R. Balakrishnan et al. [Bounds for the b-chromatic number of G−v, Discrete Appl. Math. 161 (2013) 1173-1179]. Also we show that for any connected graph G and any e ∈ E(G), b(G - e) ≤ b(G) + [...] -2. Further, we determine all graphs which attain the upper bound. Finally, we conclude by finding bound for the b-chromatic number of any subgraph.
LA - eng
KW - b-coloring; b-chromatic number; -coloring; -chromatic number
UR - http://eudml.org/doc/287091
ER -

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