Known complexity facts: the decision problem of the existence of a kernel in a digraph G = (V; E) is NP-complete; if all of the cycles of G have even length, then G has a kernel; and the question of the number of kernels is #P-complete even for this restricted class of digraphs. In the opposite direction, we construct game theory tools, of independent interest, concerning strategies in the pres...

A main aim of the workshop was to bring together the two camps, mathematicians working in combinatorial game theory and computer scientists interested in algorithmics and Artificial intelligence. The Workshop attracted a mix of people from both communities (17 from mathematics, 16 from computer science and 2 undergraduates) as well as a mixture of new and established researchers. The oldest was...

We give the first, as far as we know, feasible proof of König’s Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, and we show the equivalence of KMM to various Min-Max principles, with proofs of low complexity.

An early version of these notes was prepared for use by the participants in the Workshop on Algebra, Geometry and Topology held at the Australian National University, 22 January to 9 February, 1996. They have subsequently been updated and expanded many times for use by students in the subject 620-421 Combinatorial Group Theory at the University of Melbourne. Copyright 1996-2004 by C. F. Miller ...

Superimposed codes is a special combinatorial structure that has many applications in information theory, data communication and cryptography. On the other hand, mutually orthogonal latin squares is a beautiful combinatorial object that has deep connection with design theory. In this paper, we draw a connection between these two structures. We give explicit construction of mutually orthogonal l...