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Research Article | Open Access

Graphs that embedded in any fixed surfaces with sufficiently large maximum degree Δ is total- ( Δ + 1 )-colorable

Beijing International Cener for Mathematical Research, Peking University, Beijing 100091, China
School of Mathematical Sciences, Tongji University, Shanghai 200092, China
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Abstract

Let G be a graph that can be embedded in a surface Σ of Euler characteristic c ′ ( Σ ). In this paper, we proved that there exists an integer Δ 0 = 4 ⋅ ( 5 + 49 − 24 c ′ ) ⋅ [ 2 − c ′ + 1 2 ( 5 + 49 − 24 c ′ ) ] such that the total chromatic number of G is Δ ( G ) + 1 if Δ ( G ) ≥ Δ 0 .

Keywords

total coloringEuler characteristicsurfacemaximum degreealgebraic topology
CLC number: 05C10

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 1523-1534
DOI: 10.3934/math.2024075

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Cite this article:
Fang Q, Zhang L. Graphs that embedded in any fixed surfaces with sufficiently large maximum degree Δ is total- ( Δ + 1 )-colorable. AIMS Mathematics, 2024, 9(1): 1523-1534. https://doi.org/10.3934/math.2024075

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Received: 03 September 2023
Revised: 16 November 2023
Accepted: 21 November 2023
Published: 15 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)