On the Resilience of Bipartite Networks

Motivated by problems modeling the spread of infections in networks, in this paper we explore which bipartite graphs are most resilient to widespread infections under various parameter settings. Namely, we study bipartite networks with a requirement of a minimum degree d on one side under an independent infection, independent transmission model. We completely characterize the optimal graphs in the case d = 1, which already produces non-trivial behavior, and we give some extremal results for the more general cases. We also show that determining the subgraph of an arbitrary bipartite graph most resilient to infection is NP-hard for any one-sided minimal degree d ≥ 1.