History

Please fill in your query. A complete syntax description you will find on the General Help page.
The total chromatic number of graphs with an unique major vertex of degree four. (English)
J. Math. Res. Expo. 18, No.1, 33-38 (1998).
The total chromatic number $χ_{T}(G)$ of a graph $G$ is the least number $k$ such that $G$ has a total coloring with $k$ colors. The total coloring conjecture claims that $Δ(G)+1\leq χ_{T}(G)\leq Δ(G)+2$ for any graph $G$. A vertex $v$ of $G$ is said to be a major vertex if $d_{G}(v)=Δ(G)$. The author shows that $χ_{T}(G)=5$ for any graph $G$ with a unique major vertex of degree 4.
Reviewer: I.Tomescu (Bucureşti)