A Graph Construction Game is a Maker-Breaker game. Maker and Breaker take turns in choosing previously unoccupied edges of the complete graph KN . Maker's aim is to claim a c...
Given a weighted graph G and an error parameter > 0, the graph sparsification problem requires sampling edges in G and giving the sampled edges appropriate weights to obtain a...
: Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures...
We prove that for fixed integer D and positive reals α and γ, there exists a constant C0 such that for all p satisfying p(n) ≥ C0/n, the random graph G(n, p) asymptotically a...