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

  • Petr Kovář
  • Michael Kubesa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5874)

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.

Keywords

Span Tree Bipartite Graph Maximum Degree Complete Graph Hamiltonian Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Eldergill, P.: Decompositions of the complete graph with an even number of vertices. M.Sc. Thesis, McMaster University, Hamilton (1997)Google Scholar
  2. 2.
    Fronček, D.: Bi-cyclic Decompositions of Complete Graphs Into Spanning Trees. Discrete Math. 307, 1317–1322 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Kovářová, T.: Decompositions of Complete Graphs Into Isomorphic Spanning Trees With Given Diameters. JCMCC 54, 67–81 (2005)zbMATHGoogle Scholar
  4. 4.
    Kovářová, T.: Spanning Tree Factorizations of Complete Graphs, Ph.D. Thesis. VŠB – Technical University of Ostrava (2004)Google Scholar
  5. 5.
    Rosa, A.: On Certain Valuations of the Vertices of a Graph, Theory Graphs. In: Int. Symp. Rome 1966, pp. 349–355. Gordon and Breach, N.Y. and Dunod, Paris (1967)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Petr Kovář
    • 1
  • Michael Kubesa
    • 1
  1. 1.Department of Applied MathematicsVŠB – Technical University of OstravaOstravaCzech Republic

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