{"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/on-edge-colouring-games-by-erdos-and-bensmail","title":"On edge-colouring-games by Erdős, and Bensmail and Mc Inerney","arxiv_id":"2505.03497","date":"2025-05-06","proceeding":null,"authors":["Stijn Cambie","Michiel Provoost"],"abstract":"We study two games proposed by Erd\\H{o}s, and one game by Bensmail and Mc Inerney, all sharing a common setup: two players alternately colour edges of a complete graph, or in the biased version, they colour $p$ and $q$ edges respectively on their turns, aiming to maximise a graph parameter determined by their respective induced subgraphs. In the unbiased case, we give a first reduction towards confirming the conjecture of Bensmail and Mc Inerney, propose a conjecture for Erd\\H{o}s' game on maximum degree, and extend the clique and maximum-degree versions to edge-transitive and regular graphs. In the biased case, the maximum-degree and vertex-capturing games are resolved, and we prove the clique game with $(p,q)=(1,3)$.","url_abs":"https://arxiv.org/abs/2505.03497v1","url_pdf":"https://arxiv.org/pdf/2505.03497v1.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":"on-edge-colouring-games-by-erdos-and-bensmail","repo_url":"https://github.com/algorithmic-graph-theory-group/edge-colouring-games","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}