{"created":"2024-07-20T12:14:45.070316+00:00","id":2069403,"links":{},"metadata":{"_buckets":{"deposit":"dc2771bd-d9d8-44fa-b8c5-cdd735f653e0"},"_deposit":{"created_by":14,"id":"2069403","owners":[14],"pid":{"revision_id":0,"type":"depid","value":"2069403"},"status":"published"},"_oai":{"id":"oai:osaka-kyoiku.repo.nii.ac.jp:02069403","sets":["1706784336634:1706784822880:1708600628435:1709457859204"]},"author_link":[],"item_10002_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2002-01-31","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"153","bibliographicPageStart":"145","bibliographicVolumeNumber":"50","bibliographic_titles":[{"bibliographic_title":"大阪教育大学紀要 第III部門 : 自然科学・応用科学","bibliographic_titleLang":"ja"}]}]},"item_10002_description_6":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"In this paper, we show thate very 4-connected triangulation on the sphere can be transformed into an octahedron by a sequence of contractions of edges, preserving the 4-connectedness, and that for the projective plane and the torus, every 4-connected triangulation can be transformed into an irreducible triangulation (defined for all triangulations) by the same operations, preserving the 4-connectedness. However, for closed surfaces with high genera, there exists a 4-connected triangulation which is not irreducible and cannot be transformed into any triangulation by contracting edges, preserving the 4-connectedness.|球面の三角形分割は, 辺の縮約を繰り返すことにより, 球面の三角形分割という性質を保存して, 正四面体グラフに変形することができる. そして, 正四面体グラフのどの1辺を縮約しても, 生じるグラフは三角形分割でなくなってしまう. このようなグラフを既約三角形分割という. 球面以外の閉曲面の既約三角形分割についても, さまざまな研究が行われていて, 種数の低い閉曲面ではその具体的形が完全に決定されている. また, 球面以外の閉曲面の既約三角形分割の最小次数は4以上であることから, 最小次数4以上の三角形分割は, その最小次数条件を保存して, 既約三角形分割に変形できることが期待される. しかし, そのためには辺の縮約ともう1つの変形 (正八面対グラフの除去) が必要であった. 事実, 球面以外の閉曲面の最小次数4以上の三角形分割は, 最小次数4以上という条件を保存して, 辺の縮約と正八面対グラフの除去を繰り返して, 既約三角形分割に変形でき, さらに, 球面の最小次数4以上の三角形分割は, その2つの変形により, 正八面体グラフに変形できることが示されている. 本論文では, 任意の分離閉曲線が2-胞体を囲むという性質が成り立つ閉曲面 (すなわち, 球面, 射影平面, 卜一ラス) 上においては, 辺の縮約を繰り返すことによって, 任意の4漣結三角形分割が, 4-連結性を保存して, 既約三角形分割 (球面の場合は正八面体グラフ) に変形できることを証明した. そして, 種数の高い閉曲面では, そのような事実が成り立たないことも証明した。","subitem_description_type":"Other"}]},"item_10002_publisher_8":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"大阪教育大学","subitem_publisher_language":"ja"}]},"item_10002_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN10460897","subitem_source_identifier_type":"NCID"}]},"item_10002_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13457209","subitem_source_identifier_type":"ISSN"}]},"item_1709629085853":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"Article"}]},"item_1709629224652":{"attribute_name":"資料種別(NIIタイプ)","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_1709631006745":{"attribute_name":"TD番号","attribute_value_mlt":[{"interim":"TD00007435"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"NAKAMOTO, Atsuhiro","creatorNameLang":"ja"},{"creatorName":"ナカオト, アツヒロ","creatorNameLang":"ja-Kana"},{"creatorName":"中本, 敦浩","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"HAMA, Motoaki","creatorNameLang":"ja"},{"creatorName":"ハマ, モトアキ","creatorNameLang":"ja-Kana"},{"creatorName":"濱, 素晃","creatorNameLang":"en"}]}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"triangulation","subitem_subject_scheme":"Other"},{"subitem_subject":"edge contraction","subitem_subject_scheme":"Other"},{"subitem_subject":"octahedron","subitem_subject_scheme":"Other"},{"subitem_subject":"三角形分割","subitem_subject_scheme":"Other"},{"subitem_subject":"辺の縮約","subitem_subject_scheme":"Other"},{"subitem_subject":"正八面体グラフ","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_title":"Generating 4-Connected Triangulations on Closed Surfaces","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Generating 4-Connected Triangulations on Closed Surfaces","subitem_title_language":"en"},{"subitem_title":"閉曲面の4-連結三角形分割の生成"}]},"item_type_id":"40003","owner":"14","path":["1709457859204"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2009-04-10"},"publish_date":"2009-04-10","publish_status":"0","recid":"2069403","relation_version_is_last":true,"title":["Generating 4-Connected Triangulations on Closed Surfaces"],"weko_creator_id":"14","weko_shared_id":-1},"updated":"2024-07-20T12:14:47.945976+00:00"}