Multicoloured Random Graphs: Constructions and Symmetry

2014/06/30 by Sam Tarzi, Tarzi, Sam
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1406.7870

openalex publication_date 2014/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the emphasis is on understanding those groups that are supported by these graphs together with links with other structures such as lattices, topologies and filters, rings and algebras, metric spaces, sets and models, Moufang loops and monoids. The large amount of background material included serves as an introduction to the theories that are used to produce the new results. The large number of references should help in making this a resource for anyone interested in beginning research in this or allied fields.

Citations

• On the orbit-sizes of permutation groups containing elements separating finite subsets
• The structure of finitary permutation groups
• The Fractal Geometry of Nature
• Modular Elliptic Curves and Fermat's Last Theorem

Related

• On the automorphism group of the m-coloured random graph
• Group-Walk Random Graphs
• The random graph
• Multicoloured Random Graphs: The Random Dynamics Program
• Random Graphs: Combinatorics, Complex Networks and Disordered Systems