Pedro Araújo, Jan Hladký, Eng Keat Hng, Matas Šileikis
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Abstract Flip processes, introduced in [ Garbe, Hladký, Šileikis, Skerman: From flip processes to dynamical systems on graphons ], are a class of random graph processes defined using a rule which is just a function from all labelled graphs of a fixed order into itself. The process starts with an arbitrary given ‐vertex graph . In each step, the graph is obtained by sampling random vertices of and replacing the induced graph by . Using the formalism of dynamical systems on graphons associated to each such flip process from ibid. we study several specific flip processes, including the triangle removal flip process and its generalizations, ‘extremist flip processes’ (in which is either a clique or an independent set, depending on whether has less or more than half of all potential edges), and ‘ignorant flip processes’ in which the output does not depend on .
期刊介绍:
It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness.
Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.