An introduction to the deduction number

TL;DR

This paper introduces the deduction number, a new graph parameter for a game where searchers deduce each other's positions to capture an invisible evader, and studies its bounds across different graph classes.

Contribution

It defines the deduction number and analyzes its bounds for various graph classes, including Cartesian products, advancing understanding of pursuit-evasion games.

Findings

Upper bounds for the deduction number on Cartesian product graphs

Introduction of the deduction number as a new graph parameter

Analysis of the deduction number for different graph classes

Abstract

The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others' initial locations, but can only communicate if they are on the same vertex. Thus, searchers must deduce other searchers' movement and move accordingly. We introduce the deduction number and study it for various classes of graphs. We provide upper bounds for the deduction number of the Cartesian product of graphs.