Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W4235572053', 'doi': 'https://doi.org/10.1002/(sici)1097-0118(199809)29:1<35::aid-jgt4>3.0.co;2-f', 'title': 'Connectivity and separating sets of cages', 'display_name': 'Connectivity and separating sets of cages', 'publication_year': 1998, 'publication_date': '1998-09-01', 'ids': {'openalex': 'https://openalex.org/W4235572053', 'doi': 'https://doi.org/10.1002/(sici)1097-0118(199809)29:1<35::aid-jgt4>3.0.co;2-f'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/(sici)1097-0118(199809)29:1<35::aid-jgt4>3.0.co;2-f', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S193368155', 'display_name': 'Journal of Graph Theory', 'issn_l': '0364-9024', 'issn': ['0364-9024', '1097-0118'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5051605715', 'display_name': 'Tao Jiang', 'orcid': 'https://orcid.org/0000-0002-4359-1475'}, 'institutions': [{'id': 'https://openalex.org/I157725225', 'display_name': 'University of Illinois Urbana-Champaign', 'ror': 'https://ror.org/047426m28', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I157725225']}], 'countries': ['US'], 'is_corresponding': True, 'raw_author_name': 'Tao Jiang', 'raw_affiliation_strings': ['Department of Mathematics, University of Illinois, Urbana, IL 61801'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Illinois, Urbana, IL 61801', 'institution_ids': ['https://openalex.org/I157725225']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5079803922', 'display_name': 'Dhruv Mubayi', 'orcid': 'https://orcid.org/0000-0002-4709-8768'}, 'institutions': [{'id': 'https://openalex.org/I157725225', 'display_name': 'University of Illinois Urbana-Champaign', 'ror': 'https://ror.org/047426m28', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I157725225']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Dhruv Mubayi', 'raw_affiliation_strings': ['Department of Mathematics, University of Illinois, Urbana, IL 61801'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Illinois, Urbana, IL 61801', 'institution_ids': ['https://openalex.org/I157725225']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5051605715'], 'corresponding_institution_ids': ['https://openalex.org/I157725225'], 'apc_list': {'value': 3760, 'currency': 'USD', 'value_usd': 3760, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 1.233, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 21, 'citation_normalized_percentile': {'value': 0.874355, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 85, 'max': 86}, 'biblio': {'volume': '29', 'issue': '1', 'first_page': '35', 'last_page': '44'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10829', 'display_name': 'Networks on Chip in System-on-Chip Design', 'score': 0.9986, 'subfield': {'id': 'https://openalex.org/subfields/1705', 'display_name': 'Computer Networks and Communications'}, '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/T10829', 'display_name': 'Networks on Chip in System-on-Chip Design', 'score': 0.9986, 'subfield': {'id': 'https://openalex.org/subfields/1705', 'display_name': 'Computer Networks and Communications'}, '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/T10374', 'display_name': 'Graph Theory and Algorithms', 'score': 0.996, '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/T11797', 'display_name': 'Optical Code Division Multiple Access', 'score': 0.919, 'subfield': {'id': 'https://openalex.org/subfields/2208', 'display_name': 'Electrical and Electronic Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/cage', 'display_name': 'Cage', 'score': 0.7603206}, {'id': 'https://openalex.org/keywords/induced-subgraph', 'display_name': 'Induced subgraph', 'score': 0.51303995}, {'id': 'https://openalex.org/keywords/coherent-and-incoherent-systems', 'display_name': 'Coherent and Incoherent Systems', 'score': 0.48815}], 'concepts': [{'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.8898366}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.79007757}, {'id': 'https://openalex.org/C160272327', 'wikidata': 'https://www.wikidata.org/wiki/Q841007', 'display_name': 'Cage', 'level': 2, 'score': 0.7603206}, {'id': 'https://openalex.org/C2780990831', 'wikidata': 'https://www.wikidata.org/wiki/Q319141', 'display_name': 'Conjecture', 'level': 2, 'score': 0.6488054}, {'id': 'https://openalex.org/C132525143', 'wikidata': 'https://www.wikidata.org/wiki/Q141488', 'display_name': 'Graph', 'level': 2, 'score': 0.5433148}, {'id': 'https://openalex.org/C2778012994', 'wikidata': 'https://www.wikidata.org/wiki/Q24743362', 'display_name': 'Induced subgraph', 'level': 4, 'score': 0.51303995}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.38889045}, {'id': 'https://openalex.org/C80899671', 'wikidata': 'https://www.wikidata.org/wiki/Q1304193', 'display_name': 'Vertex (graph theory)', 'level': 3, 'score': 0.12151438}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/(sici)1097-0118(199809)29:1<35::aid-jgt4>3.0.co;2-f', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S193368155', 'display_name': 'Journal of Graph Theory', 'issn_l': '0364-9024', 'issn': ['0364-9024', '1097-0118'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4290190164', 'https://openalex.org/W4286911546', 'https://openalex.org/W4211098594', 'https://openalex.org/W3187539714', 'https://openalex.org/W2136029993', 'https://openalex.org/W2118997044', 'https://openalex.org/W2095616489', 'https://openalex.org/W2048985609', 'https://openalex.org/W2032950096', 'https://openalex.org/W2017210895'], 'abstract_inverted_index': {'A': [0, 85], '(k;': [1, 24, 61, 81, 110, 126], 'g)-cage': [2, 25, 62, 82, 111, 127], 'is': [3, 55, 67, 83, 93, 104, 128], 'a': [4, 23, 90, 94, 113, 125], 'graph': [5, 91], 'of': [6, 22, 48, 74, 96], 'minimum': [7], 'order': [8], 'among': [9], 'k-regular': [10], 'graphs': [11], 'with': [12, 36, 63], 'girth': [13], 'g.': [14], 'We': [15, 106], 'show': [16], 'that': [17, 59, 79, 100, 108, 121], 'for': [18, 43], 'every': [19, 60, 80, 109, 122], 'cutset': [20], 'S': [21], 'G,': [26], 'the': [27, 72], 'induced': [28], 'subgraph': [29], 'G[S]': [30], 'has': [31], 'diameter': [32], 'at': [33, 44], 'least': [34, 45], '⌊g/2⌋,': [35], 'equality': [37], 'only': [38], 'when': [39], 'distance': [40], '⌊g/2⌋': [41], 'occurs': [42], 'two': [46], 'pairs': [47], 'vertices': [49], 'in': [50, 89, 124], 'G[S].': [51], 'This': [52, 69], 'structural': [53], 'property': [54], 'used': [56], 'to': [57], 'prove': [58, 107, 120], 'k': [64], '≥': [65], '3': [66], '3-connected.': [68], 'result': [70], 'supports': [71], 'conjecture': [73], 'Fu,': [75], 'Huang,': [76], 'and': [77], 'Rodger': [78], 'k-connected.': [84], 'nonseparating': [86, 114], 'g-cycle': [87, 123], 'C': [88], 'G': [92, 101], 'cycle': [95], 'length': [97], 'g': [98], 'such': [99], '−': [102], 'V(C)': [103], 'connected.': [105], 'contains': [112], 'g-cycle.': [115], 'For': [116], 'even': [117], 'g,': [118], 'we': [119], 'nonseparating.': [129], '©': [130], '1998': [131, 142], 'John': [132], 'Wiley': [133], '&': [134], 'Sons,': [135], 'Inc.': [136], 'J.': [137], 'Graph': [138], 'Theory': [139], '29:': [140], '35–44,': [141]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4235572053', 'counts_by_year': [{'year': 2013, 'cited_by_count': 1}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-09-19T16:12:47.061753', 'created_date': '2022-05-12'}