The topological Tverberg theorem states that for any prime power q and continuous map from a (d + 1)(q − 1)-simplex to Rd , there are q disjoint faces Fi of the simplex whose im...
It is shown that every planar graph with no separating triangles is a subgraph of a Hamiltonian planar graph; that is, Whitney’s theorem holds without the assumption of a triang...
The f-regressive Ramsey number Rreg f (d, n) is the minimum N such that every colouring of the d-tuples of an N-element set mapping each x1, . . . , xd to a colour ≤ f(x1) contai...
We conjecture that every planar graph of odd-girth 2k + 1 admits a homomorphism to Cayley graph C(Z2k+1 2 , S2k+1), with S2k+1 being the set of (2k + 1)vectors with exactly two co...