{"type":"ScholarlyArticle","title":"Clause Learning and New Bounds for Graph Coloring","authors":[{"name":"Emmanuel Hebrard","slug":"emmanuel-hebrard","given":"Emmanuel","family":"Hebrard","affiliation":"LAAS-CNRS , Université de Toulouse , CNRS , France"},{"name":"George Katsirelos","slug":"george-katsirelos","given":"George","family":"Katsirelos","affiliation":"UMR MIA-Paris , INRA , AgroParisTech , Université Paris-Saclay , Paris , France"}],"abstract":"Graph coloring is a major component of numerous allocation and scheduling problems.\r\nWe introduce a hybrid CP/SAT approach to graph coloring based on exploring Zykov’s tree: for two non-neighbors, either they take a different color and there might as well be an edge between them, or they take the same color and we might as well merge them. Branching on whether two neighbors get the same color yields a symmetry-free tree with complete graphs as leaves, which correspond to colorings of the original graph.\r\nWe introduce a new lower bound for this problem based on Mycielskian graphs; a method to produce a clausal explanation of this bound for use in a CDCL algorithm; and a branching heuristic emulating Brelaz on the Zykov tree.\r\nThe combination of these techniques in a branch- and-bound search outperforms Dsatur and other SAT-based approaches on standard benchmarks both for finding upper bounds and for proving lower bounds.","doi":"10.24963/ijcai.2019/856","url":"https://ijcai.org/proceedings/2019/856","pdf":"https://ijcai.org/proceedings/2019/0856.pdf","markdown":"https://ijcai.org/proceedings/2019/856.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/856","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Best Sister Conferences","track":"Best Sister Conferences","number":856,"pages":{"first":6166,"last":6170},"keywords":["Constraints and SAT: SAT: Solvers and Tools","Constraints and SAT: Global Constraints","Constraints and SAT: Constraint Satisfaction"],"videos":[],"references":[{"position":1,"raw":"[Aardal et al., 2007] Karen I Aardal, Stan PM Van Hoesel, Arie MCA Koster, Carlo Mannino, and Antonio Sassano. 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