We prove a sufficient condition for a graph G to have a matching that interconnects all the components of a disconnected spanning subgraph of G. The condition is derived from a re...
In this paper, we approach the quality of a greedy algorithm for the maximum weighted clique problem from the viewpoint of matroid theory. More precisely, we consider the clique c...
There exist several theorems which state that when a matroid is representable over distinct fields 1,..., k, it is also representable over other fields. We prove a theorem, the Li...
Let M be a matroid representable over a (partial) field and B a matrix representable over a sub-partial field . We say that B confines M to if, whenever a -representation matrix ...
We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the “rando...