В рамках еженедельного Математического кружка Физтех-школы прикладной математики и информатики (ФПМИ) лекцию прочтёт доктор наук Тобиас Мюллер (Mathematical Institute of Utrecht University), специалист в области комбинаторики и случайных графов. Тема: «Logic and random graphs from minor closed classes».
A classical result of Glebskii et al. 1969 and indepently Fagin 1976 states that in the Erdos-Renyi model with edge-probability p=1/2 every graph property that can be expressed as a sentence in first order logic holds with probability tending to either zero or one.
A class of graphs is minor closed, if it is closed under the operations of removing edges and of "contracting" edges. (An example of a minor closed class of graphs is the class of all graphs that have a crossing-free drawing on some fixed surface S.)
I will discuss a recent work, joint with P. Heinig, M. Noy and A.Taraz, on analogues of the classical result of Glebskii et al./Fagin for random graphs from a minor closed class (i.e. we sample a graph uniformly at random from all graphs on n vertices from some minor closed class).
The proofs build on the major progress that was made in recent years in the study of these random graph models.
За мероприятиями ФПМИ можно следить по ссылке.
