{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/characterizing-dag-depth-of-directed-graphs","title":"Characterizing DAG-depth of Directed Graphs","arxiv_id":"1612.04980","date":"2016-12-15","proceeding":null,"authors":["Matúš Bezek"],"abstract":"We study DAG-depth, a structural depth measure of directed graphs, which naturally extends the tree-depth of ordinary graphs. We define a DAG-depth decomposition as a strategy for the cop player in the lift-free version of the cops-and-robber game on directed graphs and prove its correctness. The DAG-depth decomposition is related to DAG-depth in a similar way as an elimination tree is related to the tree-depth. We study the size aspect of DAG-depth decomposition and provide a definition of mergeable and optimally mergeable vertices in order to make the decomposition smaller and acceptable for the cop player as a strategy. We also provide a way to find the closure of a DAG-depth decomposition, which is the largest digraph for which the given decomposition represents a winning strategy for the cop player.","url_abs":"https://arxiv.org/abs/1612.04980v1","url_pdf":"https://arxiv.org/pdf/1612.04980v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"characterizing-dag-depth-of-directed-graphs","repo_url":"https://github.com/EZCodes/SoftwareEng","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}