Browsing by Author "Sun, IF"

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A study of the genus of a group
(2000-04-01)
Fu, HL
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Sun, IF
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應用數學系
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Department of Applied Mathematics
In this paper, we improve the upper bounds for the genus of the group A = Z(m1) x Z(m2) x Z(m3) (in canonical form) with at least one even mi, i = 1,2,3. As a special case, our results reproduce the known results in the cases m(3) = 3 or both ms and ms are equal to 3.
A study of typenumber in book-embedding
(2002-01-01)
Chen, YC
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Fu, HL
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Sun, IF
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應用數學系
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Department of Applied Mathematics
The type of a vertex v in a p-page book-embedding is the p x 2 matrix of nonnegative integers [GRAPHICS] where l(v,i) (respectively, r(v,i)) is the number of edges incident to v that connect on page i to vertices lying to the left (respectively, to the right) of v. The typenumber of a graph G, T(G), is the minimum number of different types among all the book-embeddings of G. In this paper, we disprove the conjecture by J. Buss et. al. which says for n greater than or equal to 4, T(L-n) is not less than 5 and prove that T(L-n) = 4 for n greater than or equal to 3.
Face 2-colorable quadrilateral embeddings of complete bipartite graphs
(2002-11-01)
Fu, HL
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Sun, IF
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應用數學系
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Department of Applied Mathematics
An embedding is said to be face 2-colorable if the faces of the embedding can be colored with two colors such that no two monochromatic faces share an edge. In this paper, it is proved that a face 2-colorable quadrilateral embedding of the complete bipartite graph K-m,K-n. exists if and only if m and n are even. Moreover, we obtain a different proof of gamma(K-m,K-n) = [(m-2)(n-2)/4] which does not use rota4 tional scheme and the methods known.
Sortabilities of partition properties
(1999)
Chang, GJ
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Chen, FL
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Huang, LL
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Hwang, FK
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Nuan, ST
Consider the partition of a set of integers into parts. Various partition properties have been proposed in the literature to facilitate the restriction of the focus of attention to some small class of partitions. Recently, Hwang, Rothblum and Yao defined and studied the sortability of these partition properties as a tool to prove the existence of a partition with such a property in a given family. In this paper we determine the sortability indices of the seven most interesting properties of partitions providing a complete solution to the sortability issue.
The typenumber of trees
(2002-06-06)
Fu, HL
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Sun, IF
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應用數學系
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Department of Applied Mathematics
This paper proves that the typenumber of a tree T is independent of the number of the pages in a book-embedding, and is equal to either D(T) or D(T) + 1, where D(T) is the set of integers which are degrees of the vertices of T. We then completely characterize trees having typenumber D(T) and trees having typenumber D(T) + 1. (C) 2002 Elsevier Science B.V. All rights reserved.