{"id":"https://openalex.org/W2094169108","doi":"https://doi.org/10.1137/040619545","title":"Labelings of Graphs with Fixed and Variable Edge-Weights","display_name":"Labelings of Graphs with Fixed and Variable Edge-Weights","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2094169108","doi":"https://doi.org/10.1137/040619545","mag":"2094169108"},"language":"en","primary_location":{"id":"doi:10.1137/040619545","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040619545","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/A5060648102","display_name":"Robert Babilon","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Robert Babilon","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005488534","display_name":"V\u00edt Jel\u00ednek","orcid":"https://orcid.org/0000-0003-4831-4079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V\u00edt Jel\u00ednek","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027559065","display_name":"Daniel Kr\u00e1l\u034f\u030c","orcid":"https://orcid.org/0000-0001-8680-0890"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Kr\u00e1l'","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072926305","display_name":"P\u00e1vel Valtr","orcid":"https://orcid.org/0000-0002-3102-4166"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pavel Valtr","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5060648102"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8216,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.85472165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"3","first_page":"688","last_page":"706"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8136452436447144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7899330854415894},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.7855562567710876},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4384641945362091},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05644071102142334}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8136452436447144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7899330854415894},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7855562567710876},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4384641945362091},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05644071102142334},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040619545","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040619545","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W205317756","https://openalex.org/W1483835096","https://openalex.org/W1557880231","https://openalex.org/W1575834508","https://openalex.org/W1967678995","https://openalex.org/W1983030532","https://openalex.org/W2029948740","https://openalex.org/W2044716204","https://openalex.org/W2056979696","https://openalex.org/W2058787498","https://openalex.org/W2072651004","https://openalex.org/W2074820146","https://openalex.org/W2076840073","https://openalex.org/W2085421834","https://openalex.org/W2116612642","https://openalex.org/W2121862002","https://openalex.org/W2133847092","https://openalex.org/W2148410650","https://openalex.org/W2154475159","https://openalex.org/W2159011960","https://openalex.org/W2184661648","https://openalex.org/W3175367423"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Motivated":[0],"by":[1,41,55,69,85],"$L(p,q)$-labelings":[2],"of":[3,9,20,32,37,39,48,51,62,65,94,122,133,156],"graphs,":[4],"we":[5],"introduce":[6],"a":[7,11,15,26,29,35,52,82,118,149],"notion":[8],"$\\lambda$-graphs:":[10],"$\\lambda$-graph":[12],"G":[13,33,40,80,161],"is":[14,34,74,112,117,141],"graph":[16],"with":[17,124,137,162],"two":[18],"types":[19],"edges:":[21],"1-edges":[22],"and":[23,59,100,103,139],"x-edges.":[24],"For":[25],"parameter":[27],"$x\\in[0,1]$,":[28],"proper":[30,83],"labeling":[31,36,84],"vertices":[38],"nonnegative":[42],"reals":[43],"such":[44,78],"that":[45,79],"the":[46,49,60,63,75,88,95,105,109,130,154],"labels":[47,61,86],"endvertices":[50,64],"1-edge":[53],"differ":[54,68],"at":[56,70],"least":[57,71],"1":[58],"an":[66],"x-edge":[67],"x;":[72],"$\\lambda_G(x)$":[73,97,111],"smallest":[76],"real":[77],"has":[81],"from":[87],"interval":[89],"$[0,\\lambda_G(x)]$.":[90],"We":[91,146],"study":[92],"properties":[93],"function":[96,110,121],"for":[98,143,158],"finite":[99,142,159],"infinite":[101],"$\\lambda$-graphs":[102,160],"establish":[104],"following":[106],"results:":[107],"if":[108],"well":[113],"defined,":[114],"then":[115],"it":[116],"piecewise":[119],"linear":[120,127],"x":[123],"finitely":[125],"many":[126],"parts.":[128],"Surprisingly,":[129],"set":[131],"$\\Lambda(\\alpha,\\beta)$":[132],"all":[134],"functions":[135,164],"$\\lambda_G$":[136],"$\\lambda_G(0)=\\alpha$":[138],"$\\lambda_G(1)=\\beta$":[140],"any":[144],"$\\alpha\\le\\beta$.":[145],"also":[147],"prove":[148],"tight":[150],"upper":[151],"bound":[152],"on":[153],"number":[155],"segments":[157],"convex":[163],"$\\lambda_G(x)$.":[165]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}