For a real c 1 and an integer n, let f(n, c) denote the maximum integer f such that every graph on n vertices contains an induced subgraph on at least f vertices in which the max...
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 ...
For any simple graph H, let σ(H, n) be the minimum m so that for any realizable degree sequence π = (d1, d2, . . . , dn) with sum of degrees at least m, there exists an n-vertex...
A spanning subgraph G of a graph H is a k-detour subgraph of H if for each pair of vertices x, y V (H), the distance, distG(x, y), between x and y in G exceeds that in H by at mo...
Nana Arizumi, Peter Hamburger, Alexandr V. Kostoch...
Let G = G(n, r) be a random geometric graph resulting from placing n nodes uniformly at random in the unit square (disk) and connecting every two nodes if and only if their Euclide...