Maximum travelling salesman problem. I

Some estimates for the optimal quality criterion for the maximum travelling salesman problem are known. These estimates are $\sim75$ % for symmetric problems and $\sim57$ % for asymmetric ones. We propose new estimates: more than $\sim(99.0$–$99.7)$ % for symmetric problems and more than $\sim(99.0$–$99.23)$ % for asymmetric problems. All estimates are obtained by extending the series of problem that occur in the solution of the maximum travelling salesman problem.