{"id":"https://openalex.org/W2093727353","doi":"https://doi.org/10.1137/11084412x","title":"The Complexity of Pebbling in Diameter Two Graphs","display_name":"The Complexity of Pebbling in Diameter Two Graphs","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2093727353","doi":"https://doi.org/10.1137/11084412x","mag":"2093727353"},"language":"en","primary_location":{"id":"doi:10.1137/11084412x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11084412x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","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/A5016956491","display_name":"Charles A. Cusack","orcid":null},"institutions":[{"id":"https://openalex.org/I145402516","display_name":"Hope College","ror":"https://ror.org/03chnr738","country_code":"US","type":"education","lineage":["https://openalex.org/I145402516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Charles A. Cusack","raw_affiliation_strings":["Department of Computer Science, Hope College, Holland, MI 49422"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hope College, Holland, MI 49422","institution_ids":["https://openalex.org/I145402516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000487658","display_name":"Timothy Lewis","orcid":null},"institutions":[{"id":"https://openalex.org/I145402516","display_name":"Hope College","ror":"https://ror.org/03chnr738","country_code":"US","type":"education","lineage":["https://openalex.org/I145402516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy Lewis","raw_affiliation_strings":["Department of Computer Science, Hope College, Holland, MI 49422"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hope College, Holland, MI 49422","institution_ids":["https://openalex.org/I145402516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030390434","display_name":"Daniel Simpson","orcid":"https://orcid.org/0000-0003-4819-2868"},"institutions":[{"id":"https://openalex.org/I145402516","display_name":"Hope College","ror":"https://ror.org/03chnr738","country_code":"US","type":"education","lineage":["https://openalex.org/I145402516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Simpson","raw_affiliation_strings":["Department of Computer Science, Hope College, Holland, MI 49422"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hope College, Holland, MI 49422","institution_ids":["https://openalex.org/I145402516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008014812","display_name":"Samuel Taggart","orcid":null},"institutions":[{"id":"https://openalex.org/I70571728","display_name":"Oberlin College","ror":"https://ror.org/05ac26z88","country_code":"US","type":"education","lineage":["https://openalex.org/I70571728"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel Taggart","raw_affiliation_strings":["Department of Mathematics, Oberlin College, Oberlin, OH 44074"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Oberlin College, Oberlin, OH 44074","institution_ids":["https://openalex.org/I70571728"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016956491"],"corresponding_institution_ids":["https://openalex.org/I145402516"],"apc_list":null,"apc_paid":null,"fwci":1.7277,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.8514388,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"3","first_page":"919","last_page":"928"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994000196456909,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8550326228141785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7621456384658813},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7337002754211426},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.6493760347366333},{"id":"https://openalex.org/keywords/pebble","display_name":"Pebble","score":0.5717280507087708},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5017733573913574},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4834074079990387},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44530290365219116}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8550326228141785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7621456384658813},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7337002754211426},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.6493760347366333},{"id":"https://openalex.org/C2777760186","wikidata":"https://www.wikidata.org/wiki/Q14673","display_name":"Pebble","level":2,"score":0.5717280507087708},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5017733573913574},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4834074079990387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44530290365219116},{"id":"https://openalex.org/C114793014","wikidata":"https://www.wikidata.org/wiki/Q52109","display_name":"Geomorphology","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/11084412x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11084412x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.hope.edu:curcp_11-1104","is_oa":false,"landing_page_url":"https://digitalcommons.hope.edu/curcp_11/105","pdf_url":null,"source":{"id":"https://openalex.org/S4306402446","display_name":"Hope College Digital Commons (Hope College)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145402516","host_organization_name":"Hope College","host_organization_lineage":["https://openalex.org/I145402516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"11th Annual Celebration of Undergraduate Research and Creative Performance (2012)","raw_type":"text"},{"id":"pmh:oai:digitalcommons.hope.edu:faculty_publications-1709","is_oa":false,"landing_page_url":"https://digitalcommons.hope.edu/faculty_publications/690","pdf_url":null,"source":{"id":"https://openalex.org/S4306402446","display_name":"Hope College Digital Commons (Hope College)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145402516","host_organization_name":"Hope College","host_organization_lineage":["https://openalex.org/I145402516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4290555974","display_name":null,"funder_award_id":"0851293","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6507447573","display_name":null,"funder_award_id":"several","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1899366296","https://openalex.org/W2003959728","https://openalex.org/W2009321501","https://openalex.org/W2013252038","https://openalex.org/W2033611584","https://openalex.org/W2081357662","https://openalex.org/W2122185950","https://openalex.org/W2133314113","https://openalex.org/W2159585659","https://openalex.org/W2741999158"],"related_works":["https://openalex.org/W1832228128","https://openalex.org/W2101259828","https://openalex.org/W2595255710","https://openalex.org/W2950657997","https://openalex.org/W2950423884","https://openalex.org/W4300915519","https://openalex.org/W2176954490","https://openalex.org/W2075903162","https://openalex.org/W4205862922","https://openalex.org/W4288115483"],"abstract_inverted_index":{"Given":[0],"a":[1,5,9,47,52,91,112],"simple,":[2],"connected":[3],"graph,":[4],"pebbling":[6,20,55],"configuration":[7,48,64,89],"is":[8,41,65,70,114],"function":[10],"from":[11,28,46],"its":[12],"vertex":[13,30,39,69,113],"set":[14],"to":[15,35,43],"the":[16,36,77,100,103],"nonnegative":[17],"integers.":[18],"A":[19,38,63],"move":[21],"between":[22],"adjacent":[23],"vertices":[24,80],"removes":[25],"two":[26,82,93],"pebbles":[27,85],"one":[29,33,59],"and":[31,83],"adds":[32],"pebble":[34,60],"other.":[37],"$r$":[40],"said":[42],"be":[44],"reachable":[45],"if":[49,67],"there":[50],"exists":[51],"sequence":[53],"of":[54,79,99,102,111,119],"moves":[56],"that":[57,86,108],"places":[58],"on":[61,76,90],"$r$.":[62],"solvable":[66],"every":[68],"reachable.":[71],"We":[72,105],"prove":[73,107],"tight":[74],"bounds":[75],"number":[78],"with":[81],"three":[84],"an":[87],"unsolvable":[88],"diameter":[92,120],"graph":[94],"can":[95],"have":[96],"in":[97,117],"terms":[98],"size":[101],"graph.":[104],"also":[106],"determining":[109],"reachability":[110],"NP-complete,":[115],"even":[116],"graphs":[118],"two.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}