This report studies problems coming from three di erent domains of theoretical computer science: Clique versus Independent set in communication complexity, the Alon-SaksSeymour conjecture in graph coloring and the stubborn problem in constraint satisfaction problem. Each problem admits a quasi-polynomial size solution, meaning of size n where n is the parameter, and the problem is to nd a polyn...

The question might not be as profound as Shakespeare’s, but nevertheless, it is interesting. Because few people seem to be aware of quasi p-groups, we will begin with a bit of history and a definition; and then we will determine for each group of order less than 24 (and a few others) whether the group is a quasi p-group for some prime p or not. This paper is a prequel to [Hwd]. In [Hwd] we prov...

Following the book [9] by Dunkl and Xu and the paper [23] by Xu we will assume that αj ≥ 0 for each j = 0, 1, . . . , k although one would expect that the range of validity can be extended analytically to the domain αj > −12 for each j. We will also exclude the case k = 1, α0 = α1 = 0 because we want the constant μ defined below in (1.5) to be positive. The parity vector p = (p0, p1, . . . , pk...