A new approach to Gal’s theory of search games on weakly eulerian networks

A network is called weakly Eulerian if it consists of a finite number of disjoint Eulerian networks which are connected in a tree-like fashion. S. Gal and others developed a theory of (zero-sum) hide-and-seek games on such networks. The minimax search time for a network is called its search value. A network is called simply searchable if its search value is half the minimum time to tour it. A celebrated result of Gal is that a network is simply searchable if and only if it is weakly Eulerian. This expository article presents a new approach to the Gal theory, based on ideas borrowed from the author's recent extension of Gal's theory to networks which can be searched at speeds depending on the location and direction in the network. Most of the proofs are new.