@article{Fang2024, 
author = {Qiming Fang and Li Zhang},
title = {Graphs that embedded in any fixed surfaces with sufficiently large maximum degree    Δ is total-   (  Δ  +  1  )-colorable},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {1523-1534},
keywords = {total coloring, Euler characteristic, surface, maximum degree, algebraic topology},
url = {https://www.sciopen.com/article/10.3934/math.2024075},
doi = {10.3934/math.2024075},
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  .}
}