Combinatorics and Graph Theory

    

Analysis of Coupling Parameters for Graph Colouring in Complex Adaptive and Dynamical Systems Framework

Authors: Shashankaditya Upadhyay

Network of oscillators are studied to understand if graph (vertex) colouring can be obtained upon synchronization when a strong negative coupling is applied between oscillators when there is an edge present in the network and a small positive coupling is applied between oscillators when there is no edge. We find that oscillators with simple equations such as Thomas' systems are best suited for such couplings. We further observe that introducing a degree of variance in coupling strength improves synchronization to a great extent in favour of returning optimal graph colouring in such networks. We further study the role of parameters (which are obtained as a result of varying coupling strength) on synchronization. The present article thus ends up proposing a polynomial time heuristic method to solve the graph colouring problem.

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[v1] 2026-08-28 19:58:00

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