Taiwanese Journal of Mathematics

THE EQUITABLE CHROMATIC THRESHOLD OF THE CARTESIAN PRODUCT OF BIPARTITE GRAPHS IS AT MOST 4

Zhidan Yan, Wu-Hsiung Lin, and Wei Wang

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Abstract

A graph $G$ is equitably $k$-colorable if its vertex set can be partitioned into $k$ independent sets, any two of which differ in size by at most 1. We prove a conjecture of Lin and Chang which asserts that for any bipartite graphs $G$ and $H$, their Cartesian product $G\Box H$ is equitably $k$-colorable whenever $k\ge 4$.

Article information

Source
Taiwanese J. Math., Volume 18, Number 3 (2014), 773-780.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706439

Digital Object Identifier
doi:10.11650/tjm.18.2014.3645

Mathematical Reviews number (MathSciNet)
MR3213385

Zentralblatt MATH identifier
1357.05047

Subjects
Primary: 05C15: Coloring of graphs and hypergraphs 05C76: Graph operations (line graphs, products, etc.)

Keywords
equitable coloring equitable chromatic threshold Cartesian product bipartite graph

Citation

Yan, Zhidan; Lin, Wu-Hsiung; Wang, Wei. THE EQUITABLE CHROMATIC THRESHOLD OF THE CARTESIAN PRODUCT OF BIPARTITE GRAPHS IS AT MOST 4. Taiwanese J. Math. 18 (2014), no. 3, 773--780. doi:10.11650/tjm.18.2014.3645. https://projecteuclid.org/euclid.twjm/1499706439


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References

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