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 ...
Abstract. For a nite multigraphG, the reliability function of G is the probability RG(q) that if each edge of G is deleted independently with probability q then the remaining edges...
We define the k-path tree matroid, and use it to solve network design problems in which the required connectivity is arbitrary for a given pair of nodes, and 1 for the other pairs...
This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more ge...