{"id":"https://openalex.org/W7220897482","doi":"https://doi.org/10.48550/arxiv.2610.09650","title":"The Almost Stacked Hypothesis: A Conjectural Analogue of Sj\u00f6strand's Cover Pebbling Theorem","display_name":"The Almost Stacked Hypothesis: A Conjectural Analogue of Sj\u00f6strand's Cover Pebbling Theorem","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220897482","doi":"https://doi.org/10.48550/arxiv.2610.09650"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09650","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09650","pdf_url":"https://arxiv.org/pdf/2610.09650","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.09650","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068767867","display_name":"Tam\u00e1s Csern\u00e1k","orcid":"https://orcid.org/0000-0002-4204-3119","observed_orcids":["https://orcid.org/0000-0002-4204-3119"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Csern\u00e1k, Tam\u00e1s","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060501499","display_name":"Lajos Soukup","orcid":"https://orcid.org/0000-0002-3975-0293","observed_orcids":["https://orcid.org/0000-0002-3975-0293"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Soukup, Lajos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9463000297546387,"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":0.9463000297546387,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.026599999517202377,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.006000000052154064,"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/graph-pebbling","display_name":"graph pebbling","score":0.9929999709129333},{"id":"https://openalex.org/keywords/stacking-number","display_name":"stacking number","score":0.9039999842643738},{"id":"https://openalex.org/keywords/cycle-graphs","display_name":"cycle graphs","score":0.5630000233650208},{"id":"https://openalex.org/keywords/trees","display_name":"trees","score":0.828000009059906},{"id":"https://openalex.org/keywords/edge-density","display_name":"edge density","score":0.7710000276565552},{"id":"https://openalex.org/keywords/hamiltonian-paths","display_name":"Hamiltonian paths","score":0.7609999775886536},{"id":"https://openalex.org/keywords/path-cover","display_name":"path cover","score":0.7739999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8460999727249146},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7042999863624573},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6866000294685364},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4964999854564667},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4821999967098236},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4521999955177307},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4327000081539154},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3643999993801117},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.32850000262260437},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C32972407","wikidata":"https://www.wikidata.org/wiki/Q1187620","display_name":"Perfect graph","level":5,"score":0.30219998955726624},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.28200000524520874},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.26739999651908875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09650","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09650","pdf_url":"https://arxiv.org/pdf/2610.09650","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.09650","doi":"https://doi.org/10.48550/arxiv.2610.09650","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09650","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09650","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09650","pdf_url":"https://arxiv.org/pdf/2610.09650","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220897482.pdf","grobid_xml":"https://content.openalex.org/works/W7220897482.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1982886989","https://openalex.org/W2013252038","https://openalex.org/W2120327434","https://openalex.org/W2911540966","https://openalex.org/W2998720439","https://openalex.org/W3049483091","https://openalex.org/W3214075858","https://openalex.org/W4225865873","https://openalex.org/W7155798658"],"related_works":["https://openalex.org/W7155798658","https://openalex.org/W7163528267","https://openalex.org/W7214715641","https://openalex.org/W3033759461","https://openalex.org/W7097856415","https://openalex.org/W2347127486","https://openalex.org/W4299668664","https://openalex.org/W2132233728","https://openalex.org/W2951798581","https://openalex.org/W2946989651"],"abstract_inverted_index":{"We":[0,43,98,173],"study":[1,124],"two":[2,194],"graph":[3,143],"pebbling":[4],"parameters,":[5],"the":[6,10,14,73,105,136,171],"stacking":[7],"number":[8,134,215],"and":[9,57,84,103,114,181,183,189],"clearing":[11,133],"number,":[12],"through":[13],"Almost":[15],"Stacked":[16],"Hypothesis":[17],"(ASH).":[18],"This":[19],"hypothesis":[20],"asserts":[21],"that":[22,45,58,80,101,117,155,167],"these":[23,77],"thresholds":[24],"can":[25],"be":[26],"determined":[27],"by":[28],"testing":[29],"only":[30,212],"configurations":[31],"in":[32,186],"which":[33,152,210],"at":[34,145],"most":[35],"one":[36,41,208],"vertex":[37],"carries":[38],"more":[39],"than":[40],"pebble.":[42],"prove":[44,99,104],"every":[46,59],"almost":[47,60],"stacked":[48,61],"configuration":[49,62],"of":[50,63,198,209,216],"size":[51,64],"$2^{n+1}-1$":[52],"on":[53,67],"$C_{2n}$":[54],"is":[55,69,149,169],"stackable":[56],"$3\\cdot":[65],"2^n-2$":[66],"$C_{2n+1}$":[68],"clearable.":[70],"Together":[71],"with":[72,144,202],"known":[74],"lower":[75],"bounds,":[76],"results":[78],"show":[79,166],"ASH":[81,111],"implies":[82],"$\\operatorname{stack}(C_{2n})=2^{n+1}-1$":[83],"$\\operatorname{clear}(C_{2n+1})=3\\cdot":[85],"2^n-2$.":[86],"For":[87],"a":[88,175,213],"finite":[89,128],"tree":[90],"$T$,":[91],"we":[92,115,123,165],"introduce":[93],"an":[94],"explicit":[95,195],"invariant":[96],"$\\operatorname{estim}(T)$.":[97],"unconditionally":[100],"$\\operatorname{stack}(T)\\geq\\operatorname{estim}(T)$":[102],"reverse":[106],"inequality":[107],"under":[108],"ASH.":[109],"Consequently,":[110],"yields":[112],"$\\operatorname{stack}(T)=\\operatorname{estim}(T)$,":[113],"conjecture":[116],"this":[118,168],"equality":[119],"holds":[120],"unconditionally.":[121],"Finally,":[122],"perfectly":[125,150,199],"pebblable":[126,200],"graphs:":[127],"connected":[129],"non-bipartite":[130],"graphs":[131,201],"whose":[132],"has":[135,211],"minimum":[137],"possible":[138],"value":[139],"$\\operatorname{clear}(G)=|V(G)|+1$.":[140],"Every":[141],"complete":[142],"least":[146],"three":[147],"vertices":[148],"pebblable,":[151],"might":[153],"suggest":[154],"perfect":[156],"pebblability":[157],"requires":[158],"high":[159],"edge":[160,203],"density.":[161],"Assuming":[162],"ASH,":[163],"however,":[164],"not":[170],"case.":[172],"give":[174],"sufficient":[176],"criterion":[177],"involving":[178],"strong":[179],"edge-triangulation":[180],"Hamiltonian-path":[182],"path-cover":[184],"conditions":[185],"vertex-deleted":[187],"subgraphs":[188],"use":[190],"it":[191],"to":[192,206],"construct":[193],"infinite":[196],"families":[197],"density":[204],"tending":[205],"zero,":[207],"linear":[214],"edges.":[217]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
