On Edge-Partitioning of Complete Geometric Graphs into Plane Trees
Hazim Michman Trao, Gek Ling Chia, Niran Abbas Ali, Adem Kılıçman · arXiv (Cornell University) · 2019
In response to a well-known open question ``Does every complete geometric graph on $2n\/$ vertices have a partition of its edge set into $n\/$ plane spanning trees?" we provide an affirmative answer when the complete geometry graph is in the regular wheel configuration. Also we present sufficient conditions for the complete geometric graph on $2n\/$ vertices to have a partition of its edge set into $n\/$ plane spanning trees (which are double stars, caterpillars or $ w\/$-caterpillars).