淡江大學機構典藏:Item 987654321/32893

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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/32893


    Title: 完全四分圖分割成3迴圈或4迴圈
    Other Titles: The study of decomposing complete 4-partite graphs into cycles of length 3 or 4
    Authors: 張哲專;Chang, Che-chuang
    Contributors: 淡江大學數學學系碩士班
    高金美;Kau, Chin-mei
    Keywords: 完全四分圖;分割;complete4-partitegraph;decompose
    Date: 2006
    Issue Date: 2010-01-11 02:56:29 (UTC+8)
    Abstract: 在本篇論文中，我們定義了：
    1.D(Kp,q,r,s)={(u,v)| Kp,q,r,s=uC3+vC4}
    2.S(Kp,q,r,s)={(u,v)| 3u+4v=|E(Kp,q,r,s)|}

    由於p,q,r,s之間的大小關係，有著各種不同情況，因此我們分別分成下列幾種情況來討論，我們證明了：
    1.D(K4(p))=S(K4(p))
    2.D(Kp,p,p,s)=S(Kp,p,p,s)
    3.當p≠4,12時,則D(Kp,p,s,s)=S(Kp,p,s,s)
    4.當p≠4,12時,則D(Kp,p,r,s)=S(Kp,p,r,s)
    5.當p、q、r、s均相異的情形時，我們獲得了下面一些結果：
    (i)當m≠4,12,u≦40m*m,則D(K2m,4m,6m,8m)=S(K2m,4m,6m,8m)
    (ii)當m≠4,12,m>n,u≦8m*m+32mn,則D(K2m,4m,6m,8n)=S(K2m,4m,6m,8n)
    (iii)當m≠4,12,m>n,u≦8m*m+32mn,則D(K2m,4m,6n,8m)=S(K2m,4m,6n,8m)
    (iv)當m≠4,12,m>n,u≦12m*m-28mn,則D(K2m,4n,6m,8m)=S(K2m,4n,6m,8m)
    (v)當m≠4,12,m>n,u≦24m*m+16mn,則D(K2n,4m,6m,8m)=S(K2n,4m,6m,8m)
    In this thesis,we define：
    1.D(Kp,q,r,s)={(u,v)| Kp,q,r,s=uC3+vC4}
    2.S(Kp,q,r,s)={(u,v)| 3u+4v=|E(Kp,q,r,s)|}

    According the relations among p,q,r,s, we have the following：
    1.D(K4(p))=S(K4(p))
    2.D(Kp,p,p,s)=S(Kp,p,p,s)
    (3) When p≠4,12 ,then D(Kp,p,s,s)=S(Kp,p,s,s)
    (4) When p≠4,12 ,then D(Kp,p,r,s)=S(Kp,p,r,s)
    (5) p,q,r,s are all different：
    (i)When m≠4,12,u≦40m*m,then D(K2m,4m,6m,8m)=S(K2m,4m,6m,8m)
    (ii)When m≠4,12,m>n,u≦8m*m+32mn,then D(K2m,4m,6m,8n)=S(K2m,4m,6m,8n)
    (iii)When m≠4,12,m>n,u≦8m*m+32mn,then D(K2m,4m,6n,8m)=S(K2m,4m,6n,8m)
    (iv)When m≠4,12,m>n,u≦12m*m-28mn,then D(K2m,4n,6m,8m)=S(K2m,4n,6m,8m)
    (v)When m≠4,12,m>n,u≦24m*m+16mn,then D(K2n,4m,6m,8m)=S(K2n,4m,6m,8m)
    Appears in Collections:[Department of Applied Mathematics and Data Science] Thesis

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