The problem of nding the minimum topology of multipro-cessing substrates supporting parallel execution of any given neighbourhood constrained system is proposed and possible optimal strategies are investigated based on the relationship between Barbosa's scheduling by edge reversal-SER-distributed algorithm and the minimum clique covering problem. It is shown that from any given clique covering ...

The second author’s ω, ∆, χ conjecture proposes that every graph satisties χ ≤ d 1 2 (∆ + 1 + ω)e. In this paper we prove that the conjecture holds for all claw-free graphs. Our approach uses the structure theorem of Chudnovsky and Seymour. Along the way we discuss a stronger local conjecture, and prove that it holds for claw-free graphs with a three-colourable complement. To prove our results ...

When you open your eyes in the morning, you usually see what you expect to see. Often it will be your bedroom, with things where you left them before you went to sleep. What if you opened your eyes and unexpectedly found yourself in a steaming tropical jungle? Why do we have expectations about what is about to happen to us? Why do we get surprised when something unexpected happens to us? More g...