The celebrated Erdős–Ko–Rado (EKR) theorem for Paley graphs of square order states that all maximum cliques are canonical in the sense that each maximum clique arises from the subfield construction. Recently, Asgarli and Yip extended this result to Peisert graphs and other Cayley graphs which are Peisert-type graphs with nice algebraic properties on the connection set. On the other hand, there are Peisert-type graphs for which the EKR theorem fails to hold. In this article, we show that the EKR theorem of Paley graphs extends to almost all pseudo-Paley graphs of Peisert-type. Furthermore, we establish the stability results of the same flavor.

This paper addresses the flight path planning problem for multiple missiles engaging stationary targets in high-risk areas. Targets protected by air defence are preferably engaged by a fleet or swarm of missiles, not individual missiles. The concept of a swarm attack is that a large number of approaching missiles overwhelm air defence. The deployment of missiles is often part of a broader mission including further participants. Flight path planning is then an integral element of mission planning, requiring strict timing coordination of all members involved. The flight times of the missiles are dictated by the master planning. We present algorithms for offline planning and online re-planning of flight paths for a fleet of missiles with flight time constraints. The algorithms are based on an advanced bidirectional RRT* algorithm that generates risk-minimizing flight paths with predefined flight times. Online planning generates the flight paths of the fleet sequentially, maintaining a safety distance between the missiles to prevent mutual collision. Offline planning uses a global optimization approach to determine an optimal selection of flight paths from a large set of potential paths. The selection is performed by a branch and bound algorithm that determines optimal cliques in the path compatibility graph. The optimization is embedded in an iterative algorithm that allows to successively improve the mission success.