The square G2 of a graph G is the graph with the same vertex set as G and with two vertices adjacent if their distance in G is at most 2. Thomassen showed that for a planar graph ...
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the pla...
The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk. Useful properties ...
We find the asymptotic number of connected graphs with k vertices and k - 1 + l edges when k, l approach infinity, reproving a result of Bender, Canfield and McKay. We use the pro...
Consider an acyclic directed network G with sources S1, S2, . . . , Sl and distinct sinks R1, R2, . . . , Rl. For i = 1, 2, . . . , l, let ci denote the min-cut between Si and Ri....