Deduction with $k$ moves

TL;DR

This paper extends the deduction game by allowing each searcher up to k moves, analyzing the impact on various graph classes to understand the strategic implications of multiple moves per searcher.

Contribution

It introduces the concept of k-move deduction number and analyzes its value across different graph classes, expanding the understanding of pursuit-evasion strategies.

Findings

Determined the k-move deduction number for paths and cycles.

Analyzed the impact of multiple moves on complete and bipartite graphs.

Explored the behavior of the k-move deduction number on Cartesian and strong product graphs.

Abstract

The deduction game may be thought of as a variant on the classical game of cops and robber in which the cops (searchers) aim to capture an invisible robber (evader); each cop is allowed to move at most once, and cops situated on different vertices cannot communicate to co-ordinate their strategy. In this paper, we extend the deduction game to allow each searcher to make $k$ moves, where $k$ is a fixed positive integer. We consider the value of the $k$-move deduction number on several classes of graphs including paths, cycles, complete graphs, complete bipartite graphs, and Cartesian and strong products of paths.