General forbidden configuration theorems

Quantum forbidden-interval theorems for stochastic resonance

We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum forbidden-interval theorem gives a necessary and sufficient condition that determines whether stochastic resonance occurs in quantum communication of classical messages. ...

Ramsey-type Theorems with Forbidden Subgraphs

A graph is called H-free if it contains no induced copy of H . We discuss the following question raised by Erdős and Hajnal. Is it true that for every graph H , there exists an ε(H) > 0 such that any H-free graph with n vertices contains either a complete or an empty subgraph of size at least n? We answer this question in the affirmative for a special class of graphs, and give an equivalent ref...

A Survey of Forbidden Configuration Results

Let F be a k×` (0,1)-matrix. We say a (0,1)-matrix A has F as a configuration if there is a submatrix of A which is a row and column permutation of F . In the language of sets, a configuration is a trace and in the language of hypergraphs a configuration is a subhypergraph. Let F be a given k × ` (0,1)-matrix. We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. The...

A Survey of Forbidden Configuration Results (Draft)

This paper surveys various results concerning the problem of forbidden configurations (also known as trace in the language of set systems). Let F be a k × ` (0,1)-matrix (the forbidden configuration). We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. The matrix F need not be simple. We define forb(m,F ) as the maximum number of columns of any simple m-rowed matri...

Configuration Theorems on Bipartite Frameworks