It is often of interest to analyse a graph in order to discover whether or not it possesses a certain property or to perform an optimization procedure upon the graph. Such an activity is often carried out by the use of an algorithm ? a recipe for the solution of a given mathematical problem. We shall discuss some algorithms for identifying the properties of a given graph, which are useful in both combinatorics and in many application areas of graph theory. We shall also discuss optimization algorithms which are often used to find the subgraph of a given weighted graph which is optimal in some sense. Both of these types of algorithms are of importance in Part II of this book.
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