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climax

Innovative

Algorithms and Complexity, is easy to verify for any given graph. But how can we really find an Euler tour in an Eulerian graph? The proof of Theorem 1.3.1 not only guarantees that such a tour exists, but actually contains a hint how to construct such a tour. We want to convert this hint into a general method for constructin

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Shortest Paths,e German motorway system in the official guide ., the railroad or bus lines in some public transportation system, and the network of routes an airline offers are routinely represented by graphs. Therefore it is obviously of great practical interest to study paths in such graphs. In particular, we of

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Spanning Trees,f trees, we then present another way of determining the number of trees on . vertices which actually applies more generally: it allows us to compute the number of spanning trees in any given connected graph. The major part of this chapter is devoted to a network optimization problem, namely to findi

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即席

Flows,network might model a system of pipelines, a water supply system, or a system of roads. With its many applications, the theory of flows is one of the most important parts of combinatorial optimization. In Chapter 7 we will encounter several applications of the theory of flows within combinatorics, a

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Combinatorial Applications,sal theory can be developed from the theory of flows on networks; this approach was first suggested in the book by Ford and Fulkerson [FoFu62] and is also used in the survey [Jun86]. Compared with the usual approach [Mir71b] of taking Philip Hall’s marriage theorem [Hal35] – which we will treat in S

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Connectivity and Depth First Search,connected components of a graph: breadth first search. In the present chapter, we mainly treat algorithmic questions concerning .-connectivity and strong connectivity. To this end, we introduce a further important strategy for searching graphs and digraphs (besides BFS), namely .. In addition, we pr

Aggressive

Colorings,the theorems of Brooks on vertex colorings and the theorem of Vizing on edge colorings. As an aside, we explain the relationship between colorings and partial orderings, and briefly discuss perfect graphs. Moreover, we consider edge colorings of Cayley graphs; these are graphs which are defined usin