A program for proving that a given graph is not a unit-distance graph: preliminary report

A graph G=(V,E) is called a unit-distance graph in the plane if there is an embedding of V into the plane such that every pair of adjacent vertices are at unit distance apart. If an embedding of V satisfies the condition that two vertices are adjacent ...

Let F be a field, and let n be a positive integer. The vertex set of the unit-quadrance graph UD(F, n) is the set of all n-tuples with entries in F; two vertices are adjacent if and only if the sum of the squares of the entries in their difference ...

At most how many edges (hyperedges, nonzero entries, characters) can a graph (hypergraph, zero-one matrix, string) have if it does not contain a fixed forbidden pattern? Turán-type extremal graph theory, Erdős--Ko--Rado-type extremal set theory, Ramsey ...