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Ars Combinatoria

  • Research article

Characterization of \(3\)-Regular Halin Graphs with Edge-face Total Chromatic Number Equal to Four

W. H. Chan1, Peter C. B. Lam2, W. C. Shiu2
1Department of Mathematics and Information Technology, The Hong Kong Institute of Education, Hong Kong
2Department of Mathematics, Hong Kong Baptist University, Hong Kong
  • Published: 31/01/2014

Abstract

The edge-face total chromatic number of \(3\)-regular Halin graphs was shown to be \(4\) or \(5\) in \([5]\). In this paper, we shall provide a necessary and sufficient condition to characterize \(3\)-regular Halin graphs with edge-face total chromatic number equal to four.

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Citation
W. H. Chan, Peter C. B. Lam, W. C. Shiu. Characterization of \(3\)-Regular Halin Graphs with Edge-face Total Chromatic Number Equal to Four[J], Ars Combinatoria, Volume 113. 257-262. .