{"created":"2025-01-19T01:34:47.361878+00:00","updated":"2025-01-19T10:07:07.137746+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00233381","sets":["1164:2592:11452:11525"]},"path":["11525"],"owner":"44499","recid":"233381","title":["ラプラシアン行列の固有値を用いた木幅の下界"],"pubdate":{"attribute_name":"公開日","attribute_value":"2024-03-14"},"_buckets":{"deposit":"3f446ea7-23c2-4a8a-afe5-cae3f0045bfb"},"_deposit":{"id":"233381","pid":{"type":"depid","value":"233381","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"ラプラシアン行列の固有値を用いた木幅の下界","author_link":["633803","633801","633804","633805","633802"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"ラプラシアン行列の固有値を用いた木幅の下界"}]},"item_type_id":"4","publish_date":"2024-03-14","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"名古屋大学"},{"subitem_text_value":"九州大学"},{"subitem_text_value":"名古屋大学"},{"subitem_text_value":"名古屋大学"},{"subitem_text_value":"名古屋大学"}]},"item_4_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Nagoya University","subitem_text_language":"en"},{"subitem_text_value":"Kyushu University","subitem_text_language":"en"},{"subitem_text_value":"Nagoya University","subitem_text_language":"en"},{"subitem_text_value":"Nagoya University","subitem_text_language":"en"},{"subitem_text_value":"Nagoya University","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_publisher":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"情報処理学会","subitem_publisher_language":"ja"}]},"publish_status":"0","weko_shared_id":-1,"item_file_price":{"attribute_name":"Billing file","attribute_type":"file","attribute_value_mlt":[{"url":{"url":"https://ipsj.ixsq.nii.ac.jp/record/233381/files/IPSJ-AL24197006.pdf","label":"IPSJ-AL24197006.pdf"},"date":[{"dateType":"Available","dateValue":"2026-03-14"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-AL24197006.pdf","filesize":[{"value":"840.8 kB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"660","billingrole":"5"},{"tax":["include_tax"],"price":"330","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"9"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"138709b9-d0de-4d17-8f7b-b0e87e7ce5da","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2024 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"儀間, 達也"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"土中, 哲秀"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"野呂, 浩平"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"小野, 廣隆"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"大舘, 陽太"}],"nameIdentifiers":[{}]}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN1009593X","subitem_source_identifier_type":"NCID"}]},"item_4_textarea_12":{"attribute_name":"Notice","attribute_value_mlt":[{"subitem_textarea_value":"SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc."}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_18gh","resourcetype":"technical report"}]},"item_4_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"2188-8566","subitem_source_identifier_type":"ISSN"}]},"item_4_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"本論文では頂点数 n，最大次数 Δ のグラフ G について，ラプラシアン行列の固有値を用いた木幅 tw(G) の下界を二つ示す．一つはラプラシアン行列の二番目に小さい固有値 λ2 を用いた下界で，tw(G)≧nλ2/(Δ+λ2)-1 が成り立つ，というものである．これは Chandran と Subramanian [A spectral lower bound for the treewidth of a graph and its consequences. Inf. Process. Lett., 87(4):195-200, 2003] によって示された下界 tw(G)≧3nλ2/(4Δ+8λ2)-1 の改善となっている．今回示した下界は，特に完全二部グラフ Ka,b に対しては tw(Ka,b)≧min{a,b}-1 を与え，Ka,b の実際の木幅 tw(Ka,b)=min{a,b} よりちょうど 1 だけ小さい値となっている．もう一つはラプラシアン行列の二番目に小さい固有値 λ2 および一番大きい固有値 λn を用いた下界で，tw(G)≧2nλ2/(3λn-λ2)-1 が成り立つ，というものである．この下界は完全グラフ Kn に対してtw(Kn)≧n-1 を与える．これは Kn の実際の木幅 tw(Kn)=n-1 と一致する．","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"2","bibliographic_titles":[{"bibliographic_title":"研究報告アルゴリズム（AL）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2024-03-14","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"6","bibliographicVolumeNumber":"2024-AL-197"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"id":233381,"links":{}}