Abstract
A substantial amount of research in graph theory continues to concentrate on the existence of hamiltonian cycles and perfect matchings. A classic theorem of Dirac states that a sufficient condition for an n-vertex graph to be hamiltonian, and thus, for n even, to have a perfect matching, is that the minimum degree is at least n/2. Moreover, there are obvious counterexamples showing that this is best possible.
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Szemerédi, E., Ruciński, A., Rödl, V. (2005). The Generalization of Dirac’s Theorem for Hypergraphs. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_5
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DOI: https://doi.org/10.1007/11549345_5
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