The vertex colouring problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it is NP-complete in any subclass of triangle-free graphs defined by a finite collection of forbidden induced subgraphs, each of which contains a cycle. In this paper, we study the vertex colouring problem in subclasses of triangle-free graphs obtained by forbidding graphs without cycles, i.e...

We study the complexity of the Graph Isomorphism problem on graph classes that are characterized by a finite number of forbidden induced subgraphs, focusing mostly on the case of two forbidden subgraphs. We show hardness results and develop techniques for the structural analysis of such graph classes, which applied to the case of two forbidden subgraphs give the following results: A dichotomy i...

HYPOTHESIS Wrong-side/wrong-site, wrong-procedure, and wrong-patient adverse events (WSPEs) are devastating, unacceptable, and often result in litigation, but their frequency and root causes are unknown. Wrong-side/wrong-site, wrong-procedure, and wrong-patient events are likely more common than realized, with little evidence that current prevention practice is adequate. DESIGN Analysis of se...