Decomposition of Geometric Graphs into Star Forests

János Pach; Morteza Saghafian; Patrick Schnider

Decomposition of Geometric Graphs into Star Forests

Combinatorics 2023-08-28 v2 Computational Geometry

Authors: János Pach , Morteza Saghafian , Patrick Schnider

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.

Keywords

graph theory

Cite

@article{arxiv.2306.13201,
  title  = {Decomposition of Geometric Graphs into Star Forests},
  author = {János Pach and Morteza Saghafian and Patrick Schnider},
  journal= {arXiv preprint arXiv:2306.13201},
  year   = {2023}
}

Comments

Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)

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