LIFO-search on digraphs: A searching game for cycle-rank

TL;DR

This paper extends a graph searching game to directed graphs, establishing that the minimal number of searchers needed equals the cycle-rank plus one, and provides a duality theorem for obstructions.

Contribution

It introduces a LIFO-search game for digraphs, proves the equivalence of game variations, and characterizes obstructions for cycle-rank with a min-max theorem.

Findings

All game variations require the same number of searchers.

Minimal searchers needed is cycle-rank plus one.

Provides a duality theorem for obstructions.

Abstract

We consider the extension of the last-in-first-out graph searching game of Giannopoulou and Thilikos to digraphs. We show that all common variations of the game require the same number of searchers, and the minimal number of searchers required is one more than the cycle-rank of the digraph. We also obtain a tight duality theorem, giving a precise min-max characterization of obstructions for cycle-rank.