I.D.Rankin, I.Underwood, D.G.Vass*, J.Gourlay*, M.R.Worboys** and M.S.Griffith** Department of Electrical Engineering, The University of Edinburgh, The Kings Buildings, Mayfield Road, Edinburgh, EH9 3JL, U.K. * Department of Physics and Astronomy, The University of Edinburgh, James Clark Maxwell Building, The Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, U.K. ** GEC-Marconi Research Centr...

Each king on an n×n chessboard is said to attack its own square and its neighboring squares, i.e., the nine or fewer squares within one move of the king. A set of kings is said to form an irredundant set if each attacks a square attacked by no other king in the set. We prove that the maximum size of an irredundant set of kings is bounded between (n− 1)=3 and n=3, and that the minimum size of a ...

5 Affiliations: 6 Institute of Evolutionary Biology, University of Edinburgh, Kings Buildings, EH9 3JT, United Kingdom 7 Present Address: Department of Genetics, University of Cambridge, Downing Street, Cambridge, 8 CB2 3EH 9 Present Address: Life Sciences, University of Sussex, United Kingdom 10 Department of Biosciences, Centre of Excellence in Biological Interactions, University of Helsinki,...

The Kings Bay, Crystal River complex, located in Citrus County, Florida, is one of the world’s largest spring-fed ecosystems and a critical warm-water refuge for endangered Florida manatees. Unfortunately, large areas of Kings Bay are currently in a state of ecological degradation characterized by smothering mats of the filamentous cyanobacterium Lyngbya wollei. The causes of this ecosystem shi...

In his paper Kings in Bipartite Hypertournaments (Graphs $\&$ Combinatorics 35, 2019), Petrovic stated two conjectures on 4-kings multipartite hypertournaments. We prove one of these and give counterexamples for the other.

A king u in a tournament is a player who beats any other player v directly or indirectly. That is, either u → v (u beats v) or there exists a third player w such that u→ w and w → v. A sorted sequence of kings in a tournament of n players is a sequence of players, S = (u1, u2, . . . , un), such that ui → ui+1 and ui in a king in sub-tournament Tui = {ui ,ui+1, . . . , un} for i = 1,2, . . . , n...