一個含有n個點的簡單圖，其中任意兩點皆有一邊相連，則稱此圖為一個完全圖，記為Kn。若一個n點的重邊圖，任意兩點皆有λ個邊相連，則稱此圖為一個λ重完全圖，記為λKn。
    一個圖H的點集合為V(H)={a,b,c,d}，邊集合為E(H)={{a,b},{a,c},{b,c},{c,d}}，則稱此圖H為箏形圖，記為(a,b,c; d)或(b,a,c; d)。
    設G1, G2, …, Gt為圖 Kn  的子圖，若滿足以下條件：
      (1) E(G1)∪E(G2)∪…∪E(Gt) = E(Kn)；
      (2) 對於1≦i≠j≦n, E(Gi)∩E(Gj) = ∅，
則稱Kn可分割成G1, G2, …, Gt。若Gi與箏形圖H同構，i=1, 2, …, n，則稱Kn可分割成箏形圖H。
    設H為Kn的子圖，且H為箏形圖，λKn可分割成箏形圖H，表示可將λKn中的所有邊分成幾個子集合，每個子集合可形成一個箏形圖H，且Kn中的任一邊出現在λ個相異箏形圖H中。
    在本篇論文中，我們證明了：
λ≡1,3  (mod 4)，且 n≡0,1 (mod 8) ⇔ λKn可分割成箏形圖。
λ≡2  (mod 4)，且 n≡0,1 (mod 4) ⇔ λKn可分割成箏形圖。
λ≡0  (mod 4)，且 ∀n≥4 ⇔ λKn可分割成箏形圖。

A simple graph with n vertices satisfies that every two vertices are joined by an edge, then we call this graph a complete graph with n vertices, denoted by Kn. If a multigraph with n vertices satisfies that every two vertices are joined by λ edges, then we call this graph a λ-fold complete graph with n vertices, denoted by λKn.
  Let H be the graph with the vertex set {a, b, c, d} and the edge set {{a, b}, {a, c}, {b, c}, {c, d}} ,we call H a kite graph, denoted by (a, b, c; d) or (b, a, c; d).
  Let G1, G2, …, Gt be subgraphs of Kn. If they satisfy the following conditions：
    (1) E(G1)∪E(G2)∪…∪E(Gt) = E(Kn)
    (2) ∀1≦i≠j≦n, E(Gi)∩E(Gj) = ∅
then we call λKn  be decomposed into G1, G2, …, Gt. If Gi is isomorphic to a graph H, for each i = 1, 2, …, n, then we call Kn be decomposed into graphs H.
  Let H be a subgraph of Kn. If all edges of λKn can be partitioned into subsets which form a kite graph H and each edge of λKn is contained in λ different kite graphs H, then we call λKn can be decomposed into kite graphs H.
  In this thesis, we proved that
(1) λ≡1,3  (mod 4) and n≡0,1 (mod 8) ⇔ λKn can be decomposed into kites.
(2) λ≡2  (mod 4) and n≡0,1 (mod 4) ⇔ λKn can be decomposed into kites.
(3) λ≡0  (mod 4) and ∀n≥4 ⇔ λKn can be decomposed into kites.

目錄
第一章	簡介	1
第二章	預備知識	2
第三章	Kn可分割成箏形圖	9
第四章	λKn可分割成箏形圖	23
第一節   2Kn可分割成箏形圖	23
第二節   3Kn可分割成箏形圖	24
第三節   4Kn可分割成箏形圖	25
第四節   λKn可分割成箏形圖	55
參考文獻	56


圖目錄
圖2.1  簡單圖	2
圖2.2  重邊圖	2
圖2.3  P4 	2
圖2.4	         3
圖2.5  C3 	3
圖2.6  K4 	3
圖2.7  K3,3	4
圖2.8  K2,2,2	5
圖2.9  箏形圖	5
圖2.10  H為G的子圖 	6
圖2.11  G可分割成G1和G2	7
圖3.1  K4,4,4分割成4個K2,2,2	10
圖3.2  K2,2,2分割成4個C3	10
圖3.3  K2,2,2分割成3個箏形圖	10
圖3.4  K8k的分割	12
圖3.5  K2k的分割	12
圖3.6  K8k的分割	15
圖3.7  K2k的分割	16
圖3.8  K8k+1的分割	18
圖3.9  K8k+1的分割	20
圖4.1  2K4	23
圖4.2  2K5	23
圖4.3  4K8k+2的分割	27
圖4.4  4K8k+2的分割	30
圖4.5  4個K3的聯集 	33
圖4.6  4K8k+3的分割	34
圖4.7  4K8k+3的分割	38
圖4.8  4K8k+6的分割	41
圖4.9  4K8k+6的分割	45
圖4.10  4K8k+7的分割	49
圖4.11  4K8k+7的分割	52

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