Disconnectedness Brings Robustness? On Network Design For Matching With Vertex Interdiction

This paper investigates sparse network designs that support large matchings under adversarial vertex deletions. We find that while connected structures (e.g., chain-type graphs) can be optimal when sparsity constraints are less stringent, disconnected structures (e.g., cluster-type graphs) can be optimal otherwise. We characterize the performance of chains and clusters to understand how the preferred design transitions from the former to the latter. Our analysis suggests that clusters are more robust to disruption, making them more advantageous in high-stress environments.