Abstract
Fronček and Kovářová provided in [2] and [3]spanning trees of order 2n that factorize K 2n for every n ≥ 2 and for every feasible diameter d, 3 ≤ d ≤ 2n − 1. We extend their work and give a spanning tree on 2n vertices with a maximum degree \({\it \Delta}\) that factorize K 2n for every n ≥ 2 and for every feasible \(2\leq {\it \Delta} \leq n\). We give a construction for both symmetric and non-symmetric spanning trees.
Research for this article was partially supported by the institutional project MSM6198910027.
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References
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Kovář, P., Kubesa, M. (2009). Factorizations of Complete Graphs into Spanning Trees with All Possible Maximum Degrees. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_33
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DOI: https://doi.org/10.1007/978-3-642-10217-2_33
Publisher Name: Springer, Berlin, Heidelberg
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