Berge's conjecture from 1982 on path partitions in directed graphs generalizes and extends Dilworth's Theorem and the Greene-Kleitman Theorem which are well known for pa...
A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a fi...
A graph G is well-covered if every maximal independent set has the same cardinality. Let sk denote the number of independent sets of cardinality k, and define the independence pol...
In 1988, Seiya Negami published a conjecture stating that a graph G has a finite planar cover (i.e. a homomorphism from some planar graph onto G which maps the vertex neighbourhoo...
We survey five mathematical discovery programs by looking in detail at the discovery processes they illustrate and the success they've had. We focus on how they estimate the ...