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In response to a well-known open question ``Does every complete geometricgraph on $2n\/$ vertices have a partition of its edge set into $n\/$ planespanning trees?" we provide an affirmative answer when the complete geometrygraph is in the regular wheel configuration. Also we present sufficientconditions for the complete geometric graph on $2n\/$ vertices to have apartition of its edge set into $n\/$ plane spanning trees (which are doublestars, caterpillars or $ w\/$-caterpillars).

On Edge-Partitioning of Complete Geometric Graphs into Plane Trees