2023/12/31 by Pelekis, Christos
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2401.00543
Fix a positive integer n, a real number p∈ (0,1], and a (perhaps random) hypergraph H on [n]. We introduce and investigate the following random multigraph model, which we denote \mathbbG(n,p ; H): begin with an empty graph on n vertices, which are labelled by the set [n]. For every H∈ H choose, independently from previous choices, a doubleton from H, say D = \i,j\ ⊂ H, uniformly at random and then introduce an edge between the vertices i and j in the graph with probability p, where each edge is introduced independently of all other edges.