In the composite hypothesis testing setting, the detector receives n i.i.d. samples either from a distribution p∈P or from a distribution q∈Q. It then decides the correct set from which the samples were drawn.
What is the largest number of edges in a graph of order n and girth g? For d-regular graphs, essentially the best known answer is provided by the Moore bound. This result can be extended to cover irregular graphs as well.
In any tournament between several participants, transitivity is sometimes not satisfied (i.e. A may defeat B, B defeats C and C in turn defeats A). In any case, we shall have to define a winner.
