Edge-Face Total Chromatic Number of Halin Graphs

W. H. Chan; Peter C. B. Lam; W. C. Shiu

doi:10.1137/070687988

Edge-Face Total Chromatic Number of Halin Graphs

W. H. Chan, Peter C. B. Lam, W. C. Shiu

Department of Mathematics

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

6 Citations (Scopus)

27 Downloads (Pure)

Abstract

We show that the edge-face total chromatic number of Halin graphs with maximum vertex degree Δ not less than 4 is equal to max{5, Δ}. For the cases of Δ = 4 and 5, we provide a proper 5-edge-face total coloring algorithm.

Original language	English
Pages (from-to)	1646-1654
Number of pages	9
Journal	SIAM Journal on Discrete Mathematics
Volume	23
Issue number	3
DOIs	https://doi.org/10.1137/070687988
Publication status	Published - 11 Nov 2009

Scopus Subject Areas

General Mathematics

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Edge-face total chromatic number
Halin graphs

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10.1137/070687988

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title = "Edge-Face Total Chromatic Number of Halin Graphs",

abstract = "We show that the edge-face total chromatic number of Halin graphs with maximum vertex degree Δ not less than 4 is equal to max{5, Δ}. For the cases of Δ = 4 and 5, we provide a proper 5-edge-face total coloring algorithm.",

keywords = "Edge-face total chromatic number, Halin graphs",

author = "Chan, {W. H.} and Lam, {Peter C. B.} and Shiu, {W. C.}",

note = "Funding information: This work was partially supported by Faculty Research Grant (FRG/07-08/II-30), Hong Kong Baptist University, and CERG (HKBU210207), Research Grant Council, Hong Kong. Publisher copyright: Copyright {\textcopyright} 2009 Society for Industrial and Applied Mathematics",

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AB - We show that the edge-face total chromatic number of Halin graphs with maximum vertex degree Δ not less than 4 is equal to max{5, Δ}. For the cases of Δ = 4 and 5, we provide a proper 5-edge-face total coloring algorithm.

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Edge-Face Total Chromatic Number of Halin Graphs

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