Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established ...

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

KATARZYNA RYBARCZYK, DUDLEY STARK, POISSON APPROXIMATION OF THE NUMBER OF CLIQUES IN RANDOM INTERSECTION GRAPHS, Journal of Applied Probability, Vol. 47, No. 3 (SEPTEMBER 2010), pp. 826-840 ...

Abstract.For two vertices 𝑢 and 𝑣 of a graph 𝐺, the set 𝐼[𝑢, 𝑣] consists of all vertices lying on some 𝑢 - 𝑣 geodesic in 𝐺. If 𝑆 is a set of vertices of 𝐺, then 𝐼[𝑆] is the union of all ...