Dining Philosophers and Graph Covering Problems

Let the vertices of a graph denote processes in a distributed or time-shared computer system; let two vertices be connected by an edge if the two processes cannot proceed at the same time (they mutually exclude one another). Managing mutual exclusion and related scheduling problems has given rise to substantial literature in computer science. Some methods of attack include covering or partitioning the graph with cliques or threshold graphs. Here I survey some recent graph-theoretic results and examples motivated by this approach.