{"_buckets": {"deposit": "c2dbffd4-7ac9-4738-b99a-b9832c08f954"}, "_deposit": {"id": "2005207", "owners": [1], "pid": {"revision_id": 0, "type": "depid", "value": "2005207"}, "status": "published"}, "_oai": {"id": "oai:repository.dl.itc.u-tokyo.ac.jp:02005207", "sets": []}, "author_link": [], "item_4_biblio_info_7": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2020-11-06", "bibliographicIssueDateType": "Issued"}, "bibliographicIssueNumber": "1", "bibliographicPageEnd": "156", "bibliographicPageStart": "109", "bibliographicVolumeNumber": "27", "bibliographic_titles": [{"bibliographic_title": "Journal of Mathematical Sciences The University of Tokyo", "bibliographic_titleLang": "en"}]}]}, "item_4_description_5": {"attribute_name": "\u6284\u9332", "attribute_value_mlt": [{"subitem_description": "Let $\\Gamma$ be a chart, and we denote by $\\Gamma_m$ the union of all the edges of label $m$. A chart $\\Gamma$ is of type $(m;2,3,2)$ if $w(\\Gamma)=7$, $w(\\Gamma_m\\cap\\Gamma_{m+1})=2$, $w(\\Gamma_{m+1}\\cap\\Gamma_{m+2})=3$, and $w(\\Gamma_{m+2}\\cap\\Gamma_{m+3})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we prove that if there is a minimal chart $\\Gamma$ of type $(m;2,3,2)$, then each of $\\Gamma_{m+1}$ and $\\Gamma_{m+2}$ contains one of three kinds of graphs. In the next paper, we shall prove that there is no minimal chart of type $(m;2,3,2)$. ", "subitem_description_language": "en", "subitem_description_type": "Abstract"}]}, "item_4_publisher_20": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "Graduate School of Mathematical Sciences, The University of Tokyo", "subitem_publisher_language": "en"}]}, "item_4_source_id_10": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "attribute_value_mlt": [{"subitem_source_identifier": "AA11021653", "subitem_source_identifier_type": "NCID"}]}, "item_4_source_id_8": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "13405705", "subitem_source_identifier_type": "ISSN"}]}, "item_4_text_17": {"attribute_name": "Mathmatical Subject Classification", "attribute_value_mlt": [{"subitem_text_language": "en", "subitem_text_value": "57Q45(MSC2010)"}, {"subitem_text_language": "en", "subitem_text_value": "57Q35(MSC2010)"}]}, "item_4_text_33": {"attribute_name": "\u539f\u7a3f\u53d7\u9818\u65e5", "attribute_value_mlt": [{"subitem_text_value": "2020-04-07"}]}, "item_4_text_4": {"attribute_name": "\u8457\u8005\u6240\u5c5e", "attribute_value_mlt": [{"subitem_text_language": "en", "subitem_text_value": "Tokai University"}, {"subitem_text_language": "en", "subitem_text_value": "Department of Mathematics, Tokai University"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorAffiliations": [{"affiliationNames": [{"affiliationName": "Tokai University", "affiliationNameLang": "en"}]}], "creatorNames": [{"creatorName": "Nagase , Teruo", "creatorNameLang": "en"}]}, {"creatorAffiliations": [{"affiliationNames": [{"affiliationName": "Tokai University", "affiliationNameLang": "en"}]}], "creatorNames": [{"creatorName": "Shima, Akiko", "creatorNameLang": "en"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"date": [{"dateType": "Available", "dateValue": "2022-06-23"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "jms270106.pdf", "filesize": [{"value": "677.8 KB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 677800.0, "url": {"objectType": "fulltext", "url": "https://repository.dl.itc.u-tokyo.ac.jp/record/2005207/files/jms270106.pdf"}, "version_id": "48b18fdb-a3f6-4f83-a6f6-213ab2e5c9eb"}]}, "item_keyword": {"attribute_name": "\u30ad\u30fc\u30ef\u30fc\u30c9", "attribute_value_mlt": [{"subitem_subject": "Surface link", "subitem_subject_language": "en", "subitem_subject_scheme": "Other"}, {"subitem_subject": "chart", "subitem_subject_language": "en", "subitem_subject_scheme": "Other"}, {"subitem_subject": "white vertex", "subitem_subject_language": "en", "subitem_subject_scheme": "Other"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Properties of Minimal Charts and their Applications VI : The Graph {\\Large$\\boldsymbol{\\Gamma_{m+1}}$} in a Chart {\\Large$\\boldsymbol{\\Gamma}$} of Type {\\Large$\\boldsymbol{(m;2,3,2)}$", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Properties of Minimal Charts and their Applications VI : The Graph {\\Large$\\boldsymbol{\\Gamma_{m+1}}$} in a Chart {\\Large$\\boldsymbol{\\Gamma}$} of Type {\\Large$\\boldsymbol{(m;2,3,2)}$", "subitem_title_language": "en"}]}, "item_type_id": "4", "owner": "1", "path": ["312/6865/1655967293406/1655967376130", "9/504/6868/1655967151838/1655967215050"], "permalink_uri": "http://hdl.handle.net/2261/0002005207", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2022-06-23"}, "publish_date": "2022-06-23", "publish_status": "0", "recid": "2005207", "relation": {}, "relation_version_is_last": true, "title": ["Properties of Minimal Charts and their Applications VI : The Graph {\\Large$\\boldsymbol{\\Gamma_{m+1}}$} in a Chart {\\Large$\\boldsymbol{\\Gamma}$} of Type {\\Large$\\boldsymbol{(m;2,3,2)}$"], "weko_shared_id": -1}