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Hamiltonian coloring is a type of graph coloring. Hamiltonian coloring uses a concept called detour distance between two vertices of the graph. It has many applications in different areas of science and technology.
Detour distance
The distance between two vertices in a graph is defined as the minimum of lengths of paths connecting those vertices. The detour distance between two vertices, say, u and v is defined as the length of the longest u-v path in the graph. In the case of a tree the detour distance between any two vertices is same as the distance between the two vertices.
References
Hamiltonian coloring Wikipedia(Text) CC BY-SA