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姓名 謝孟萍(Hsieh, Meng-Ping) 查詢紙本館藏 畢業系所 數學系 論文名稱
(The 3-split of multipaths and multicycles with multiplicity 2)相關論文 檔案 [Endnote RIS 格式] [Bibtex 格式] [相關文章] [文章引用] [完整記錄] [館藏目錄] [檢視] [下載]
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摘要(中) 令G為一個圖(graph),若G的邊(edges)可分解成t個同構之子圖,則此t個子圖稱為G的t-split,且稱G是可t分解的(t-splittable)。
在這個論文裡,我們證明了以下的結果。
一、 設Q為一個重邊數為2,且總邊數可被3整除的多重路徑(multipaths),則Q為可三分解的。
二、 設C為一個重邊數為2,且總邊數可被3整除的多重圈(multicycles),則C為可三分解的。
摘要(英) Let G be a graph and t be a positive integer. A t-split of G is a partition of the edges of G into t isomorphic subgraphs. A graph is said to be t-splittable if
it has a t-split.
In this thesis we prove the following results.
Theorem. Let Q be a multipath with multiplicity 2 such that jE(Q)j=0 (mod 3). Then Q is 3-splittable.
Theorem. Let C be a multicycle with multiplicity 2 such that jE(C)j=0 (mod 3). Then C is 3-splittable.關鍵字(中) ★ 圖形三分解 關鍵字(英) ★ 3-split 論文目次 1. Introduction to t-splits of graphs ...................1
2. 3-splits of multipaths with mutiplicity 2.............4
3. 3-splits of multicycles with mutiplicity 2 ..........15
References..............................................18參考文獻 [1] Y.-R. Chen, Two Edge Labelings in Graphs : Graph Decomposition and Antimagic Labeling, Ph.D Thesis (2013).
[2] F. Harary, R.W. Robinson and N.C. Wormald, The Divisibility theorem for isomorphic factorization of complete graphs, J.G.T. 1 (1977) 187-188.
[3] F. Harary, R.W. Robinson and N.C. Wormald, Isomorphic factorization III : Complete multipartite graphs, Combinatorial Math., Lecture Notes in Math.686 (1978) 47-54.
[4] R.E. Jamison and G.E. Stevens, Isomorphic factorizations of caterpillars, Congr. Numer. 158 (2002) 143-151.
[5] J. Knisely, C. Wallis and G. Domke, The partitioned graph isomorphism problem, Congr. Numer. 89 (1992) 39-44.
[6] S.T. Quinn, Isomorphic factorizations of complete equipartite graphs, J.G.T. 7 (1983) 285-310.
[7] G.E. Stevens, Properties of Lucas trees, Ars Combin. 92 (2009) 171-192.
[8] V.G. Vizig, On an estimate of the chromatic class of a P-graph (Rus.), Diskret. Analiz 3 (1967) 25-30.指導教授 林強(Chiang Lin) 審核日期 2014-7-2 推文 facebook plurk twitter funp google live udn HD myshare reddit netvibes friend youpush delicious baidu 網路書籤 Google bookmarks del.icio.us hemidemi myshare