Decomposition of Geometric Graphs into Star-Forests

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János Pach, Morteza Saghafian, Patrick Schnider

Published: 01 Jan 2023, Last Modified: 22 May 2024GD (1) 2023EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than \(n-1\) star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.