Temporal Ramsey Graphs: Ramsey Kinematic Approach to the Motion of Systems of Material Points

We propose the Ramsey approach for the analysis of the kinematics of the systems built of non-relativistic, motile point masses/particles. The approach is based on the colored graphs theory. Point masses/particles serve as the vertices of the graph. The time dependence of the distance between the particles determines the coloring of the links. The vertices/particles are connected with an orange link, when the particles move away from each other or remain at the same distance. The vertices/particles are linked with the violet edge, when the particles converge. The sign of the time derivative of the distance between the particles dictates the color of the edge. Thus, the complete, bi-colored, Ramsey, temporal graph emerges. The suggested coloring procedure is not transitive. The coloring of the link is time dependent. The proposed coloring procedure is frame independent and insensitive to Galilean transformations. At least one monochromatic triangle will inevitably appear in the graph emerging from the motion of six particles, due to the fact that the Ramsey number R(3,3)=6. The approach is extended for the analysis of the systems, containing infinite number of the moving point masses. Infinite monochromatic (violet or orange) clique will necessarily appear in the graph.