2018/07/30 by Nelson, Peter, van der Pol, Jorn
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1807.11383
A biased graph is a graph G, together with a distinguished subset B of its cycles so that no Theta-subgraph of G contains precisely two cycles in B. A large number of biased graphs can be constructed by choosing G to be a complete graph, and B to be an arbitrary subset of its Hamilton cycles. We show that, on the logarithmic scale, the total number of simple biased graphs on n vertices does not asymptotically exceed the number that can be constructed in this elementary way.