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Fundamental Groups of Neighborhood Complexes
http://hdl.handle.net/2261/00074893
http://hdl.handle.net/2261/000748935ad67d1e-244d-4a6d-93dd-32f642c0e181
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms240302.pdf (223.9 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2018-07-17 | |||||
| タイトル | ||||||
| タイトル | Fundamental Groups of Neighborhood Complexes | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Graphs | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | graph homomorphisms | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | neighborhood complexes | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | fundamental groups | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | departmental bulletin paper | |||||
| 著者 |
Matsushita, Takahiro
× Matsushita, Takahiro |
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| 著者所属 | ||||||
| 値 | Department of Mathematics, Kyoto University | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | 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. | |||||
| 書誌情報 |
Journal of Mathematical Sciences The University of Tokyo 巻 24, 号 3, p. 321-353, 発行日 2017-07-14 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| 著者版フラグ | ||||||
| 値 | publisher | |||||
| Mathmatical Subject Classification | ||||||
| 値 | 55Q05(MSC2010) | |||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 値 | 2016-02-12 | |||||
