Control and optimization theory

Linear convex graphs and some route game problems

E. G. Belov

Chelyabinsk State University

Abstract: A generalization by means of the linear norm for the notion of convex set is considered in the paper. The concept is transferred to finite graphs. Properties of such graphs are studied by means of resolution of the open Traveling Salesman Problem and some route games in the conflict condition on them.

Keywords: convex set, quasiconvex function, linear norm, Hamiltonian circuit, Traveling Salesman Problem, zero-sum game.