Edge-face Total Chromatic Number of 3-Regular Halin Graphs

Peter Che Bor Lam; Wai Chee Shiu; Wai Hong Chan

Edge-face Total Chromatic Number of 3-Regular Halin Graphs

Peter Che Bor Lam
, Wai Chee Shiu
, Wai Hong Chan

Department of Mathematics

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

Abstract

A Halin graph is a plane graph H = T ∪ C, where T is a plane tree with no vertex of degree two and at least one vertex of degree three or more, and C is a cycle connecting the end vertices of T in the cyclic order determined by a plane embedment of T. In this paper, we show that if G is a 3-regular Halin graph, then 4 ≤ χ_ef(G) ≤ 5; and these bounds are sharp.

Original language	English
Pages (from-to)	161-165
Number of pages	5
Journal	Congressus Numerantium
Volume	145
Publication status	Published - Dec 2000

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Edge-face total chromatic number
Halin graph

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title = "Edge-face Total Chromatic Number of 3-Regular Halin Graphs",

abstract = "A Halin graph is a plane graph H = T ∪ C, where T is a plane tree with no vertex of degree two and at least one vertex of degree three or more, and C is a cycle connecting the end vertices of T in the cyclic order determined by a plane embedment of T. In this paper, we show that if G is a 3-regular Halin graph, then 4 ≤ χef (G) ≤ 5; and these bounds are sharp.",

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

author = "Lam, \{Peter Che Bor\} and Shiu, \{Wai Chee\} and Chan, \{Wai Hong\}",

note = "Funding information: Partially supported by Faculty Research Grant, Hong Kong Baptist University; and Research Grant Council Grant, Hong Kong",

year = "2000",

month = dec,

language = "English",

volume = "145",

pages = "161--165",

journal = "Congressus Numerantium",

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T1 - Edge-face Total Chromatic Number of 3-Regular Halin Graphs

AU - Lam, Peter Che Bor

AU - Shiu, Wai Chee

AU - Chan, Wai Hong

N1 - Funding information: Partially supported by Faculty Research Grant, Hong Kong Baptist University; and Research Grant Council Grant, Hong Kong

PY - 2000/12

Y1 - 2000/12

N2 - A Halin graph is a plane graph H = T ∪ C, where T is a plane tree with no vertex of degree two and at least one vertex of degree three or more, and C is a cycle connecting the end vertices of T in the cyclic order determined by a plane embedment of T. In this paper, we show that if G is a 3-regular Halin graph, then 4 ≤ χef (G) ≤ 5; and these bounds are sharp.

AB - A Halin graph is a plane graph H = T ∪ C, where T is a plane tree with no vertex of degree two and at least one vertex of degree three or more, and C is a cycle connecting the end vertices of T in the cyclic order determined by a plane embedment of T. In this paper, we show that if G is a 3-regular Halin graph, then 4 ≤ χef (G) ≤ 5; and these bounds are sharp.

KW - Edge-face total chromatic number

KW - Halin graph

M3 - Journal article

SN - 0384-9864

VL - 145

SP - 161

EP - 165

JO - Congressus Numerantium

JF - Congressus Numerantium

ER -

Edge-face Total Chromatic Number of 3-Regular Halin Graphs

Abstract

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