In this paper we investigate the behaviour of subgraphs of sparse ε-regular bipartite graphs G = (V1 ∪ V2, E) with vanishing density d that are induced by small subsets of vertices. In particular, we show that, with overwhelming probability, a random set S ⊆ V1 of size s 1/d contains a subset S′ with |S′| ≥ (1 − ε′)|S| that induces together with V2 an ε′-regular bipartite graph of density (1 ± ...

Editor—Sydor and colleagues studied trainee behaviour in a crisis situation, and trainee ability to challenge a decision by a consultant anaesthetist to administer blood to a patient who is a Jehovah’s Witness. This was described as unethical, although perhaps a better term would be ‘in breach of the law’. I would like to put it to the authors that unless the notes were shown to contain the pro...