Local resilience of graphs

TL;DR

This paper systematically studies the local resilience of graphs, especially random and pseudo-random graphs, to understand how much local modification is needed to destroy certain properties, leading to new challenging problems.

Contribution

It introduces a formal framework for graph resilience and provides sharp results for random and pseudo-random graphs, advancing understanding of their structural robustness.

Findings

Established sharp bounds for local resilience in random graphs

Extended resilience analysis to pseudo-random graphs

Identified new open problems in graph robustness

Abstract

In this paper, we initiate a systematic study of graph resilience. The (local) resilience of a graph G with respect to a property P measures how much one has to change G (locally) in order to destroy P. Estimating the resilience leads to many new and challenging problems. Here we focus on random and pseudo-random graphs and prove several sharp results.