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* Corresponding author Abstract—The research aims to generate a sparse graph for travelling salesman problem so as to reduce its complexity. A probability model based on frequency quadrilaterals is given to show that the average frequency of an edge is 3N if its total frequency is computed with N random frequency quadrilaterals in complete graph ࡷ ࢔. For an edge in the optimal Hamiltonian cycle, the minimum frequency is derived as ቀ૜ ൅ ૛ ࢔૛ ቁࡺ .It suggests we can throw away the edges with frequency below ቀ૜ ൅ ૛ ࢔૛ ቁࡺ and still keep the optimal Hamiltonian cycle in the reserved graph. We test the probability model with quitea few Euclidean TSP instances. The results show the thresholdቀ૜ ൅ ૛ ࢔૛ ቁ ࡺis too small for most of the instances.

A Probability Model Based on Frequency Quadrilaterals for Travelling Salesman Problem