**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32131

##### Total Chromatic Number of Δ-Claw-Free 3-Degenerated Graphs

**Authors:**
Wongsakorn Charoenpanitseri

**Abstract:**

**Keywords:**
Total colorings,
the total chromatic number,
3-degenerated.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1316590

**References:**

[1] M. Behzad, The total chromatic number of a graph Combinatorial Mathematics and its Applications, Proceedings of the Conference Oxford Academic Press N. Y. 1-9, 1971.

[2] V. G. Vizing, On evaluation of chromatic number of a p-graph (in Russian) Discrete Analysis, Collection of works of Sobolev Institute of Mathematics SB RAS 3 3-24, 1964.

[3] X. Zhou, Y. Matsuo, T. Nishizeki, List total colorings of series-parallel Graphs, Computing and Combinatorics,Lecture Notes in Comput. Sci. 2697, Springer Berlin, 172-181, 2003.

[4] M. Rosenfeld, On the total coloring of certain graphs. Israel J. Math. 9 396-402, 1971.

[5] N. Vijayaditya, On total chromatic number of a graph, J. London Math. Soc. 3 405-408, 1971.

[6] H. P. Yap, Total colourings of graphs. Bull. London Math. Soc. 21 159-163, 1989.

[7] A. V. Kostochka, The total colorings of a multigraph with maximal degree 4. Discrete Math. 17, 161-163, 1977.

[8] A. V. Kostochka, Upper bounds of chromatic functions of graphs (in Russian). Doctoral Thesis, Novosibirsk, 1978.

[9] A. V. Kostochka, Exact upper bound for the total chromatic number of a graph (in Russian). In: Proc. 24th Int. Wiss. Koll.,Tech. Hochsch. Ilmenau,1979 33-36, 1979.

[10] H. P. Yap, Total coloring of graphs, Lecture Note in Mathematics Vol. 1623, Springer Berlin, 1996.

[11] R. L. Brooks, On coloring the nodes of a network, Proc. Cambridge Phil. Soc. 37 194-197, 1941.

[12] D. B. West, Introduction to Graph Theory, Prentice Hall, New Jersey, 2001.

[13] S. Fiorini, R. J. Wilson, Edge Coloring of Graphs, Pitman London, 1977.

[14] M. Bezhad, G. Chartrand, J. K. Cooper, The colors numbers of complete graphs, J. London Math. Soc. 42 225-228, 1967.