We present a deterministic way of assigning small (log bit) weights to the edges of a bipartite planar graph so that the minimum weight perfect matching becomes unique. The isolati...
Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n 3k - 2 then m k(n - k), and for n 3k - 1 an equality is possible if, and only if, G is t...
Eroh and Oellermann defined BRR(G1, G2) as the smallest N such that any edge coloring of the complete bipartite graph KN,N contains either a monochromatic G1 or a multicolored G2....
Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least n2 edges have to be deleted from it to make it H-free. It is known that in this ca...
We examine several online matching problems, with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G, with partite sets L, R. We...