We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K 2m,2m , a result connected to a conjecture of Graham and Häggkvist. The result also implies that asymptotically almost surely a tree with m edges decomposes the complete graph with O(m 2) edges. An ingredient of the proof consists in showing that the bipartition classes of the base tree of a ...

The induced restricted versions of the vector space Ramsey theorem and of the Graham-Rothschild parameter set theorem are proved.

Graham-Little syndrome, also know as Graham-Little-Piccardi-Lassueur syndrome, is an unusual form of lichen planopilaris, characterized by the presence of cicatricial alopecia on the scalp, keratosis pilaris of the trunk and extremities, and non-cicatricial hair loss of the pubis and axillae. We present the case of a 47-year-old woman whose condition was unusual in that there was a prominence o...

In 1961 G. Higman proved a remarkable theorem establishing a deep connection between the logical notion of recursiveness and questions about finitely presented groups. The basic aim of the present paper is to provide the reader with a rigorous and detailed proof of Higman’s Theorem. All the necessary preliminary material, including elements of group theory and recursive functions theory, is sys...

We propose a new, logical, approach to the decidability problem for the Straubing and Brzozowski hierarchies based on the preservation theorems from model theory, on a theorem of Higman, and on the Rabin tree theorem. In this way, we get purely logical, short proofs for some known facts on decidability, which might be of methodological interest. Our approach is also applicable to some other sim...