Geodesic
Interval non-total colorable graphs
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2015), pp. 37-41

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A total coloring of a graph $G$ is a coloring of its vertices and edges such that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. An interval total $t$-coloring of a graph $G$ is a total coloring of $G$ with colors $1,2,\dots,t$ such that all colors are used, and the edges incident to each vertex $v$ together with $v$ are colored by $d_G(v)+ 1$ consecutive colors, where $d_G(v)$ is the degree of a vertex $v$ in $G$. In this paper we describe some methods for constructing of graphs that have no interval total coloring.
Keywords: total coloring, interval total coloring, interval coloring. 
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N. A. Khachatryan. Interval non-total colorable graphs. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2015), pp. 37-41. http://geodesic.mathdoc.fr/item/UZERU_2015_3_a5/