Packing Plane Spanning Trees and Paths in Complete Geometric Graphs

We consider the following question: How many edgedisjoint plane spanning trees are contained in a complete geometric graph GKn on any set S of n points in general position in the plane?

[1]  Franz Aurenhammer,et al.  Enumerating Order Types for Small Point Sets with Applications , 2002, Order.

[2]  W. T. Tutte.  On the Problem of Decomposing a Graph into n Connected Factors , 1961 .

[3]  Subhash Suri,et al.  Applications of a semi-dynamic convex hull algorithm , 1990, BIT.

[4]  Géza Tóth,et al.  Geometric Graphs with Few Disjoint Edges , 1998, SCG '98.

[5]  Patrick Schnider.  Packing Plane Spanning Double Stars into Complete Geometric Graphs , 2016 .

[6]  David R. Wood,et al.  Edge-Removal and Non-Crossing Configurations in Geometric Graphs , 2010, Discret. Math. Theor. Comput. Sci..

[7]  Marc Noy,et al.  Bipartite Embeddings of Trees in the Plane , 1999, Discret. Appl. Math..

[8]  David Eppstein,et al.  Journal of Graph Algorithms and Applications Geometric Thickness of Complete Graphs , 2022 .

[9]  P. Erdös.  On Sets of Distances of n Points , 1946 .

[10]  Gyula Károlyi,et al.  Ramsey-Type Results for Geometric Graphs, I , 1997, Discret. Comput. Geom..

[11]  Paul C. Kainen,et al.  The book thickness of a graph , 1979, J. Comb. Theory, Ser. B.

[12]  Sukhamay Kundu,et al.  Bounds on the number of disjoint spanning trees , 1974 .

[13]  Prosenjit Bose,et al.  Partitions of Complete Geometric Graphs into Plane Trees , 2004, GD.

[14]  Micha A. Perles,et al.  Blockers for Noncrossing Spanning Trees in Complete Geometric Graphs , 2013 .

[15]  C. Nash-Williams.  Edge-disjoint spanning trees of finite graphs , 1961 .

[16]  Wayne Goddard,et al.  Crossing families , 1991, SCG '91.

[17]  Jakub Černý,et al.  Geometric Graphs with No Three Disjoint Edges , 2005, Discret. Comput. Geom..

[18]  Eduardo Rivera-Campo.  A Note on the Existence of Plane Spanning Trees of Geometric Graphs , 1998, JCDCG.

[19]  Zdenek Dvorak,et al.  Noncrossing Hamiltonian paths in geometric graphs , 2007, Discret. Appl. Math..

[20]  János Pach,et al.  Ramsey-type results for geometric graphs , 1996, SCG '96.

[21]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.