Hamiltonian coloring

Hamiltonian coloring is a concept in graph theory related to both Hamiltonian cycles and proper graph coloring. Specifically, a Hamiltonian coloring of a graph is a way of assigning colors to the vertices of a graph such that: 1. The graph contains a Hamiltonian cycle, which is a cycle that visits each vertex exactly once. 2. Adjacent vertices (those connected by an edge) in the Hamiltonian cycle must receive different colors.