Factorizations of Complete Graphs into Spanning Trees with All Possible Maximum Degrees

  • Authors:

  • Petr Kovář;Michael Kubesa

  • Affiliations:

  • Department of Applied Mathematics, VŠB --- Technical University of Ostrava, Ostrava, Czech Republic 708 33;Department of Applied Mathematics, VŠB --- Technical University of Ostrava, Ostrava, Czech Republic 708 33

  • Venue:
  • Combinatorial Algorithms
  • Year:
  • 2009

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Abstract

Fron驴ek and Kovářová provided in [2] and [3]spanning trees of order 2n that factorize K 2n for every n 驴 2 and for every feasible diameter d, 3 ≤ d ≤ 2n 驴 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 驴 2 and for every feasible $2\leq {\it \Delta} \leq n$. We give a construction for both symmetric and non-symmetric spanning trees.