{"created":"2021-03-01T07:10:42.931461+00:00","id":49772,"links":{},"metadata":{"_buckets":{"deposit":"100501b2-8662-4c63-9082-529c11b5cd6e"},"_deposit":{"id":"49772","owners":[],"pid":{"revision_id":0,"type":"depid","value":"49772"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00049772","sets":["312:6865:7726:7842","9:504:6868:7728:7843"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2017-07-14","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"3","bibliographicPageEnd":"353","bibliographicPageStart":"321","bibliographicVolumeNumber":"24","bibliographic_titles":[{"bibliographic_title":"Journal of Mathematical Sciences The University of Tokyo"}]}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"The neighborhood complexes of graphs were introduced by Lovász in his proof of the Kneser conjecture. He showed that a certain topological property of $N(G)$ gives a lower bound for the chromatic number of $G$. In this paper, we study a combinatorial description of the fundamental groups of the neighborhood complexes. For a positive integer $r$, we introduce the $r$-fundamental group $\\pi_1^r(G,v)$ of a based graph $(G,v)$ and the $r$-neighborhood complex $N_r(G)$ of $G$. The $1$-neighborhood complex is the neighborhood complex. We show that the even part $\\pi_1^{2r}(G,v)_{ev}$, which is a subgroup of $\\pi_1^{2r}(G,v)$ with index 1 or 2, is isomorphic to the fundamental group of $(N_r(G),v)$ if $v$ is not isolated. We can use the $r$-fundamental groups to show the non-existence of graph homomorphisms. For example, we show that $\\pi_1^3(KG_{2k+1,k})$ is isomorphic to $\\mathbb{Z} / 2$, and this implies that there is no graph homomorphism from $KG_{2k+1,k}$ to the 5-cycle graph $C_5$. We discuss the covering maps associated to $r$-fundamental groups.","subitem_description_type":"Abstract"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_4_select_14":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_select_item":"publisher"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","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_value":"55Q05(MSC2010)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"2016-02-12"}]},"item_4_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematics, Kyoto University"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Matsushita, Takahiro"}],"nameIdentifiers":[{"nameIdentifier":"147756","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-07-17"}],"displaytype":"detail","filename":"jms240302.pdf","filesize":[{"value":"223.9 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms240302.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/49772/files/jms240302.pdf"},"version_id":"40a810b3-6452-4fdb-a180-4b750d3570e8"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Graphs","subitem_subject_scheme":"Other"},{"subitem_subject":"graph homomorphisms","subitem_subject_scheme":"Other"},{"subitem_subject":"neighborhood complexes","subitem_subject_scheme":"Other"},{"subitem_subject":"fundamental groups","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Fundamental Groups of Neighborhood Complexes","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Fundamental Groups of Neighborhood Complexes"}]},"item_type_id":"4","owner":"1","path":["7842","7843"],"pubdate":{"attribute_name":"公開日","attribute_value":"2018-07-17"},"publish_date":"2018-07-17","publish_status":"0","recid":"49772","relation_version_is_last":true,"title":["Fundamental Groups of Neighborhood Complexes"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:15:48.291655+00:00"}