Algorithmic Aspects of Perfect Graphs

This chapter presents algorithmic aspects of perfect graphs and surveys a number of topics in algorithmic graph theory that involve classes of perfect graphs. Algorithmic complexity analysis deals with the quantitative aspects of problem solving. It addresses the issue of what can be computed within a practical or reasonable amount of time and space by measuring the resource requirements exactly or by obtaining upper and lower bounds for them. Various priorities can be established to guide the choice of candidates, and each priority will yield a slightly different algorithm. If candidates are stored in a queue, then single spanning tree (SST) gives a breadth-first search (BFS) of G. Storing candidates in a stack SST does a depth-first search (DFS). If the edges have costs associated with them, and if the candidate with minimum cost is always chosen, then SST produces a minimum cost-spanning tree (MST).