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Equitable critical graphs

A proper vertex coloring of a graph [Formula: see text] is equitable if the sizes of any two color classes differ by at most one. The equitable chromatic number of a graph [Formula: see text], denoted by [Formula: see text], is the minimum [Formula: see text] such that [Formula: see text] is equitably [Formula: see text]-colorable. In this paper, we discuss some basic properties of equitable critical graphs as well as equitable [Formula: see text]-critical graphs. A graph [Formula: see text] is called equitable critical if [Formula: see text] for every proper subgraph [Formula: see text] of [Formula: see text]. [Formula: see text] is called equitable [Formula: see text]-critical if it is equitable [Formula: see text]-chromatic and equitable critical. Furthermore, we discuss that equitable vertex (edge) critical, equitable critical vertex (edge) graphs.

World Scientific Pub Co Pte Ltd

Loura Jency Benedict Michael Raj

Discrete Mathematics, Algorithms and Applications

2022

Title: Equitable critical graphs

Description:

A proper vertex coloring of a graph [Formula: see text] is equitable if the sizes of any two color classes differ by at most one.

The equitable chromatic number of a graph [Formula: see text], denoted by [Formula: see text], is the minimum [Formula: see text] such that [Formula: see text] is equitably [Formula: see text]-colorable.

In this paper, we discuss some basic properties of equitable critical graphs as well as equitable [Formula: see text]-critical graphs.

A graph [Formula: see text] is called equitable critical if [Formula: see text] for every proper subgraph [Formula: see text] of [Formula: see text].

[Formula: see text] is called equitable [Formula: see text]-critical if it is equitable [Formula: see text]-chromatic and equitable critical.

Furthermore, we discuss that equitable vertex (edge) critical, equitable critical vertex (edge) graphs.

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