A result on total coloring of circulant graph
Abstract
In this work we determine that all members of an infinite family of 4-regular circulant graphs are Type 1.
Keywords:
Total coloring, regular graphs, circulant graphs
References
Behzad, M. (1965). Graphs and their chromatic numbers. PhD thesis, Michigan University.
Campos, C. (2006). O problema da coloração total em classes de grafos. PhD thesis, University of Campinas, São Paulo.
Chetwynd, A. G. and Hilton, A. J. W. (1988). Some refinements of the total chromatic number conjecture. Congr. Numer., pages 195–216.
Hackmann, A. and Kemnitz, A. (2004). Circular total colorings of cubic circulant graphs. J. Combin. Math. Combin. Comput., pages 65–72.
Khennoufa, R. and Togni, O. (2008). Total and fractional total colourings of circulant grap. Discrete Math., pages 6316–3329.
Vizing, V. (1968). Some unsolved problems in graph theory. Russian Math. Surveys, 23:125–141.
Yap, H. (1996). Total colourings of graphs. Springer, Berlin.
Zorzi, A. (2019). Coloração total em grafos potências de ciclo. Master’s thesis, Federal University of Rio de Janeiro.
Campos, C. (2006). O problema da coloração total em classes de grafos. PhD thesis, University of Campinas, São Paulo.
Chetwynd, A. G. and Hilton, A. J. W. (1988). Some refinements of the total chromatic number conjecture. Congr. Numer., pages 195–216.
Hackmann, A. and Kemnitz, A. (2004). Circular total colorings of cubic circulant graphs. J. Combin. Math. Combin. Comput., pages 65–72.
Khennoufa, R. and Togni, O. (2008). Total and fractional total colourings of circulant grap. Discrete Math., pages 6316–3329.
Vizing, V. (1968). Some unsolved problems in graph theory. Russian Math. Surveys, 23:125–141.
Yap, H. (1996). Total colourings of graphs. Springer, Berlin.
Zorzi, A. (2019). Coloração total em grafos potências de ciclo. Master’s thesis, Federal University of Rio de Janeiro.
Published
2020-06-30
How to Cite
ALVES JUNIOR, Mauro N.; SASAKI, Diana.
A result on total coloring of circulant graph. In: PROCEEDINGS OF THE THEORY OF COMPUTATION MEETING (ETC), 5. , 2020, Cuiabá.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2020
.
p. 81-84.
ISSN 2595-6116.
DOI: https://doi.org/10.5753/etc.2020.11095.
