[{"article_number":"16","citation":{"ieee":"M. H. Henzinger and P. Peng, “Constant-time Dynamic (Δ +1)-Coloring,” ACM Transactions on Algorithms, vol. 18, no. 2. Association for Computing Machinery (ACM), 2022.","short":"M.H. Henzinger, P. Peng, ACM Transactions on Algorithms 18 (2022).","ama":"Henzinger MH, Peng P. Constant-time Dynamic (Δ +1)-Coloring. ACM Transactions on Algorithms. 2022;18(2). doi:10.1145/3501403","apa":"Henzinger, M. H., & Peng, P. (2022). Constant-time Dynamic (Δ +1)-Coloring. ACM Transactions on Algorithms. Association for Computing Machinery (ACM). https://doi.org/10.1145/3501403","mla":"Henzinger, Monika H., and Pan Peng. “Constant-Time Dynamic (Δ +1)-Coloring.” ACM Transactions on Algorithms, vol. 18, no. 2, 16, Association for Computing Machinery (ACM), 2022, doi:10.1145/3501403.","ista":"Henzinger MH, Peng P. 2022. Constant-time Dynamic (Δ +1)-Coloring. ACM Transactions on Algorithms. 18(2), 16.","chicago":"Henzinger, Monika H, and Pan Peng. “Constant-Time Dynamic (Δ +1)-Coloring.” ACM Transactions on Algorithms. Association for Computing Machinery (ACM), 2022. https://doi.org/10.1145/3501403."},"user_id":"72615eeb-f1f3-11ec-aa25-d4573ddc34fd","article_processing_charge":"No","author":[{"orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","last_name":"Henzinger","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"Pan","full_name":"Peng, Pan","last_name":"Peng"}],"title":"Constant-time Dynamic (Δ +1)-Coloring","acknowledgement":"We want to thank an anonymous referee who pointed out a mistake in our conference paper as well as suggesting a fix using an approach in References.","quality_controlled":"1","publisher":"Association for Computing Machinery (ACM)","year":"2022","publication":"ACM Transactions on Algorithms","day":"04","date_created":"2022-07-27T10:58:53Z","date_published":"2022-03-04T00:00:00Z","doi":"10.1145/3501403","_id":"11662","type":"journal_article","article_type":"original","status":"public","date_updated":"2022-07-27T11:08:13Z","extern":"1","abstract":[{"text":"We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (Δ +1)-vertex coloring of a graph with maximum degree at most Δ. This improves upon the previous O(log Δ)-time algorithm by Bhattacharya et al. (SODA 2018). Our algorithm uses an approach based on assigning random ranks to vertices and does not need to maintain a hierarchical graph decomposition. We show that our result does not only have optimal running time but is also optimal in the sense that already deciding whether a Δ-coloring exists in a dynamically changing graph with maximum degree at most Δ takes Ω (log n) time per operation.","lang":"eng"}],"oa_version":"None","scopus_import":"1","intvolume":" 18","month":"03","publication_status":"published","publication_identifier":{"eissn":["1549-6333"],"issn":["1549-6325"]},"language":[{"iso":"eng"}],"volume":18,"issue":"2"}]