Decomposition of Geometric Graphs into Star Forests

Published 22 Jun 2023 in math.CO and cs.CG | (2306.13201v2)

Abstract: We solve a problem of Dujmovi\'c 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.

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