Modeling K-coteries by well-covered graphs

The concept of k-coterie is useful for achieving k-mutual exclusion in distributed systems. A graph is said to be well covered if any of its maximal independent sets is also maximum. We first show that a graph G is well covered with independence number k if and only if G represents the incidence relation among quorums forming a k-coterie. We then discuss the problem of constructing k-coteries having some desirable properties. We also characterize the well-covered graphs with independence number 2.