Induced subgraphs of powers of oriented cycles

TL;DR

This paper generalizes a matrix-based approach to analyze the properties of induced subgraphs within powers of oriented cycles, extending previous results related to hypercube graphs.

Contribution

It introduces a $q$-analogue of Huang's 'magic' matrix to study Cartesian powers of directed cycles, broadening the scope of the sensitivity conjecture analysis.

Findings

Generalization of Huang's matrix to directed cycles

Extension of sensitivity conjecture techniques to new graph classes

New insights into the structure of powers of oriented cycles

Abstract

By using a $q$-analogue of the "magic" matrix introduced by H.Huang in his elegant solution of the sensitivity conjecture, we give a direct generalization of his result, replacing a hypercube graph by a Cartesian power of a directed $l$-cycle.