A subquadratic certification scheme for P5-free graphs

TL;DR

This paper presents a new subquadratic local certification scheme for verifying P5-freeness in graphs, reducing certificate size to O(n^{3/2}), which is a significant improvement over previous bounds.

Contribution

It introduces the first subquadratic certificate size bound for P5-freeness in local certification of graphs.

Findings

Achieved an O(n^{3/2}) upper bound on certificate size for P5-freeness.

First subquadratic certification scheme for this property.

Advances understanding of local certification complexity for graph properties.

Abstract

In local certification, vertices of a $n$-vertex graph perform a local verification to check if a given property is satisfied by the graph. This verification is performed thanks to certificates, which are pieces of information that are given to the vertices. In this work, we focus on the local certification of $P_5$-freeness, and we prove a $O(n^{3/2})$ upper bound on the size of the certificates, which is (to our knowledge) the first subquadratic upper bound for this property.