{"id":"https://openalex.org/W13416703","doi":"https://doi.org/10.1007/978-3-642-03409-1_8","title":"Martingales on Trees and the Empire Chromatic Number of Random Trees","display_name":"Martingales on Trees and the Empire Chromatic Number of Random Trees","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W13416703","doi":"https://doi.org/10.1007/978-3-642-03409-1_8","mag":"13416703"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-03409-1_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-03409-1_8","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022238950","display_name":"Colin Cooper","orcid":"https://orcid.org/0000-0002-5264-4401"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Colin Cooper","raw_affiliation_strings":["Department of Computer Science, Kings\u2019 College, London, UK","Department of Computer Science, Kings' College, London, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Kings\u2019 College, London, UK","institution_ids":["https://openalex.org/I183935753"]},{"raw_affiliation_string":"Department of Computer Science, Kings' College, London, UK#TAB#","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028143491","display_name":"Andrew R. A. McGrae","orcid":null},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andrew R. A. McGrae","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool, UK","Department of Computer Science University of Liverpool Liverpool UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"Department of Computer Science University of Liverpool Liverpool UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013505086","display_name":"Michele Zito","orcid":null},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michele Zito","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool, UK","Department of Computer Science University of Liverpool Liverpool UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"Department of Computer Science University of Liverpool Liverpool UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.4118,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.94560669,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"74","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6344550848007202},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6264127492904663},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.6020129323005676},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5873741507530212},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5268638730049133},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4957447946071625},{"id":"https://openalex.org/keywords/empire","display_name":"Empire","score":0.4801439940929413},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4667905271053314},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45663076639175415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42697736620903015},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4201945662498474},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.06606116890907288}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6344550848007202},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6264127492904663},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6020129323005676},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5873741507530212},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5268638730049133},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4957447946071625},{"id":"https://openalex.org/C2778495208","wikidata":"https://www.wikidata.org/wiki/Q48349","display_name":"Empire","level":2,"score":0.4801439940929413},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4667905271053314},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45663076639175415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42697736620903015},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4201945662498474},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.06606116890907288},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-642-03409-1_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-03409-1_8","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.182.3168","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.3168","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.kcl.ac.uk/staff/ccooper/papers/color.pdf","raw_type":"text"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/18eca370-625f-495b-a42e-28e9596300fd","is_oa":false,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/18eca370-625f-495b-a42e-28e9596300fd","pdf_url":null,"source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cooper, C, McGrae, A R A & Zito, M 2009, Martingales on Trees and the Empire Chromatic Number of Random Trees. in 17th International Symposium on Fundamentals of Computation Theory. vol. 5699 LNCS, FUNDAMENTALS OF COMPUTATION THEORY, PROCEEDINGS, BERLIN, pp. 74 - 83, 17th International Symposium on Fundamentals of Computation Theory, Wroclaw, Poland, 2/09/2009.","raw_type":"contributionToPeriodical"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2826816524","display_name":null,"funder_award_id":"EP/D059372/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W599250420","https://openalex.org/W1558737914","https://openalex.org/W1599622173","https://openalex.org/W1965399019","https://openalex.org/W1978113428","https://openalex.org/W1985000598","https://openalex.org/W1985250014","https://openalex.org/W2006544720","https://openalex.org/W2012526406","https://openalex.org/W2021304992","https://openalex.org/W2060664509","https://openalex.org/W2114475148","https://openalex.org/W2165387581","https://openalex.org/W2295428206","https://openalex.org/W2479149412","https://openalex.org/W2800024591","https://openalex.org/W4231916799","https://openalex.org/W4241950961","https://openalex.org/W4252334863","https://openalex.org/W4256453260"],"related_works":["https://openalex.org/W2003592880","https://openalex.org/W3181863426","https://openalex.org/W2063786047","https://openalex.org/W2562533332","https://openalex.org/W656927711","https://openalex.org/W421021154","https://openalex.org/W2081086472","https://openalex.org/W1485662969","https://openalex.org/W2306553012","https://openalex.org/W4230311663"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
