{"article_number":"102186","date_published":"2025-12-01T00:00:00Z","external_id":{"arxiv":["2306.13201"]},"title":"Decomposition of geometric graphs into star-forests","author":[{"first_name":"János","full_name":"Pach, János","last_name":"Pach"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza"},{"first_name":"Patrick","full_name":"Schnider, Patrick","last_name":"Schnider"}],"month":"12","oa_version":"Preprint","quality_controlled":"1","article_type":"original","article_processing_charge":"No","corr_author":"1","citation":{"ista":"Pach J, Saghafian M, Schnider P. 2025. Decomposition of geometric graphs into star-forests. Computational Geometry. 129, 102186.","chicago":"Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric Graphs into Star-Forests.” <i>Computational Geometry</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.comgeo.2025.102186\">https://doi.org/10.1016/j.comgeo.2025.102186</a>.","short":"J. Pach, M. Saghafian, P. Schnider, Computational Geometry 129 (2025).","apa":"Pach, J., Saghafian, M., &#38; Schnider, P. (2025). Decomposition of geometric graphs into star-forests. <i>Computational Geometry</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2025.102186\">https://doi.org/10.1016/j.comgeo.2025.102186</a>","ama":"Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. <i>Computational Geometry</i>. 2025;129. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2025.102186\">10.1016/j.comgeo.2025.102186</a>","ieee":"J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” <i>Computational Geometry</i>, vol. 129. Elsevier, 2025.","mla":"Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.” <i>Computational Geometry</i>, vol. 129, 102186, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2025.102186\">10.1016/j.comgeo.2025.102186</a>."},"abstract":[{"lang":"eng","text":"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."}],"language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2025.102186","acknowledgement":"A preliminary version of this note has been published in the proceedings of the 31st International Symposium on Graph Drawing and Network Visualization, Palermo, 2023. The authors would like to thank the anonymous referees for their valuable comments.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","publication_identifier":{"issn":["0925-7721"]},"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"15012"}]},"OA_type":"green","publication_status":"published","_id":"21253","date_created":"2026-02-16T15:48:42Z","publication":"Computational Geometry","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.13201","open_access":"1"}],"publisher":"Elsevier","volume":129,"date_updated":"2026-02-17T13:14:39Z","status":"public","OA_place":"repository","arxiv":1,"day":"01","department":[{"_id":"HeEd"}],"type":"journal_article","intvolume":"       129","oa":1}