Abstract
The matching problem is an important combinatorial problem defined on a graph. Graphs provide very often a pictorial representation of the mathematical structure underlying combinatorial optimization problems. On the other hand, graph theory is by itself rich of elegant results that can give us useful insights on many combinatorial and physical problems. For these reasons, we present here a very short introduction to the basic definitions and results of graph theory. We will refer mostly to the standard textbook of Diestel [3].
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Notes
- 1.
In the present work, given a set A of \(N\in \mathbb {N}\) elements, we will use the notation \(|A|=N\) for the cardinality of the set.
- 2.
More general polynomial algorithms are available to solve the matching problem on weighted graph \(\mathtt {K}_{N,M}\), \(N\ne M\).
- 3.
Observe that different matching solutions are in general possible, but corresponding to the same cost.
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Sicuro, G. (2017). Graphs and Optimization. In: The Euclidean Matching Problem. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-46577-7_2
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DOI: https://doi.org/10.1007/978-3-319-46577-7_2
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