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The total chromatic number of pseudo-outerplanar graphs

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Abstract

A planar graph G is called a (-pseudo-outerplanar graph if there is a subset Vo ⊆ V(G), |Vo| = i, such that G-V o is an outerplanar graph. In particular, when G-V o is a forest. G is called a:i-pseudo-tree. In this paper, the following results are proved: (i) The conjecture on the total coloring is true for all 1-pseudo-outerplanar graphs; (ii) X i (G) = Δ(G) + 1 for any 1-pseudo-outerplanar graph G with Δ(G’) ≥ 6 and for any 1-pseudo-tree G with Δ(G) ≥ 3. where X, (G) is the total chromatic number of a graph G.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, 210093, Nanjing

    Wang Weifan & Zhang Kemin

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  1. Wang Weifan
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  2. Zhang Kemin
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The project is supported by NSFC, NSFJS and NSFLNEC

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Weifan, W., Kemin, Z. The total chromatic number of pseudo-outerplanar graphs. Appl. Math. Chin. Univ. 12, 455–462 (1997). https://doi.org/10.1007/s11766-997-0048-1

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  • DOI: https://doi.org/10.1007/s11766-997-0048-1

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