Escape and Evasion on Finite Graphs

TL;DR

This paper introduces a new two-player game on finite graphs involving escape and capture strategies, analyzes its computational complexity, and explores potential simplifications and attacker requirements.

Contribution

It defines a novel game model on graphs, proves its PSPACE-completeness for bounded moves, and investigates attacker strategies and simplifications.

Findings

The game is PSPACE-complete with a move limit.

Potential methods to simplify the problem are discussed.

Analysis of attacker requirements on various graph types.

Abstract

In this paper we will be introducing a type of game which as far as this author is aware has never been studied before. These are games where there are two players, one who is trying to get one of his pieces, called a King to a predefined escape vertex, and the other, called attackers, who is trying to capture him by occupying all of his neighbours. We will be showing that this game is PSpace-complete if it is limited to $M$ moves and taking a brief look at some potential ways to simplify the problem and work out how many attackers are needed to capture the King on different types of graphs.