Abstract
The perfect 1-factorization conjecture by A. Kotzig [7] asserts the existence of a 1-factorization of a complete graph K 2n in which any two 1-factors induce a Hamiltonian cycle. This conjecture is one of the prominent open problems in graph theory.Apart from its theoretical significance it has a number of applications, particularly in designing topologies for wireless communication.Recently, a weaker version of this conjecture has been proposed in [1] for the case of semi-perfect 1-factorizations. A semi-perfect 1-factorization is a decomposition of a graph G into distinct 1-factors F 1, ..., F k such that F 1∪ F i forms a Hamiltonian cycle for any 1 < i ≤ k.We show that complete graphs K 2n , hypercubes Q 2n + 1 and tori T 2n × 2n admit a semi-perfect 1-factorization.
Supported in part by grant APVT-20-018902.
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Královič, R., Královič, R. (2005). On Semi-perfect 1-Factorizations. In: Pelc, A., Raynal, M. (eds) Structural Information and Communication Complexity. SIROCCO 2005. Lecture Notes in Computer Science, vol 3499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11429647_18
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DOI: https://doi.org/10.1007/11429647_18
Publisher Name: Springer, Berlin, Heidelberg
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