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The Network Simplex Algorithm,ts trying to apply this algorithm also to problems from graph theory. Indeed, the most important network optimization problems may be formulated in terms of linear programs; this holds, for instance, for the determination of shortest paths, maximal flows, optimal flows, and optimal circulations. Nev

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https://doi.org/10.1007/978-3-531-91853-2r some basic aspects of graph theoretic algorithms such as, for example, the problem of how to represent a graph. Moreover, we need a way to formulate the algorithms we deal with. We shall illustrate and study these concepts quite thoroughly using two specific examples, namely Euler tours and acycli

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https://doi.org/10.1007/978-3-663-14591-2e German motorway system in the official guide, the railroad or bus lines in a 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 often

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https://doi.org/10.1007/978-3-663-14368-0nt chapter, we will study this important class of graphs in considerably more detail. After some further characterizations of trees, we shall study another way of determining the number of trees on . vertices which actually applies more generally: it allows one to compute the number of spanning tree