On the equitable chromatic number of complete n-partite graphs

Peter Che Bor Lam; Wai Chee SHIU; Chong Sze TONG; Zhong Fu Zhang

doi:10.1016/S0166-218X(00)00296-1

On the equitable chromatic number of complete n-partite graphs

Peter Che Bor Lam^*, Wai Chee SHIU, Chong Sze TONG, Zhong Fu Zhang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

17 Citations (Scopus)

23 Downloads (Pure)

Abstract

In this note, we derive an explicit formula for the equitable chromatic number of a complete n-partite graph K_p1,p₂,...,p_n. Namely, if M is the largest integer such thatp_i(modM)<p_iM(i=1,2,...,n)thenχ _e(K_p1,p₂,...,p_n)=∑i=1np _iM+1,where χ_e(G) is the equitable chromatic number of graph G.

Original language	English
Pages (from-to)	307-310
Number of pages	4
Journal	Discrete Applied Mathematics
Volume	113
Issue number	2-3
DOIs	https://doi.org/10.1016/S0166-218X(00)00296-1
Publication status	Published - 15 Oct 2001

Scopus Subject Areas

Discrete Mathematics and Combinatorics
Applied Mathematics

User-Defined Keywords

05C15
68Q20
Complete n-partite graphs
Equitable chromatic number

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10.1016/S0166-218X(00)00296-1

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title = "On the equitable chromatic number of complete n-partite graphs",

abstract = "In this note, we derive an explicit formula for the equitable chromatic number of a complete n-partite graph Kp1,p2,...,pn. Namely, if M is the largest integer such thatpi(modM)iM(i=1,2,...,n)thenχ e(Kp1,p2,...,pn)=∑i=1np iM+1,where χe(G) is the equitable chromatic number of graph G.",

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author = "Lam, {Peter Che Bor} and SHIU, {Wai Chee} and TONG, {Chong Sze} and Zhang, {Zhong Fu}",

note = "Funding Information: This work was partially supported by RGC, Hong Kong, and FRG, Hong Kong Baptist University. ",

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AU - SHIU, Wai Chee

AU - TONG, Chong Sze

AU - Zhang, Zhong Fu

N1 - Funding Information: This work was partially supported by RGC, Hong Kong, and FRG, Hong Kong Baptist University.

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AB - In this note, we derive an explicit formula for the equitable chromatic number of a complete n-partite graph Kp1,p2,...,pn. Namely, if M is the largest integer such thatpi(modM)iM(i=1,2,...,n)thenχ e(Kp1,p2,...,pn)=∑i=1np iM+1,where χe(G) is the equitable chromatic number of graph G.

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ER -

On the equitable chromatic number of complete n-partite graphs

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