2020/01/15 by McDiarmid, Colin
#05C40 #05C80 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2001.05256
Let the class A of graphs be bridge-addable; that is, whenever a graph G in A has vertices u and v in different components then the graph G+uv is in A. For a random graph sampled uniformly from the graphs in A on vertex set 1,..,n, there are known lower bounds on the probability of being connected (for example, the probability is always at least 1/e). We ask here about similar results when the random graph is sampled uniformly from the unlabelled n-vertex graphs in A.