Abstract
A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ″(G) is the smallest integer k such that G has a total k-coloring. In this paper, it is proved that the total chromatic number of any graph G embedded in a surface Σ of Euler characteristic χ(Σ) ⩾ 0 is Δ(G) + 1 if Δ(G) ⩾ 10, where Δ(G) denotes the maximum degree of G.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
