Browsing by Author "Fu, HL"

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1-rotationally resolvable 4-cycle systems of 2K(v)
(2002)
Fu, HL
;
Mishima, M
;
應用數學系
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Department of Applied Mathematics
In this article, it is shown that there exists a 1-rotationally resolvable 4-cycle system of 2K(v). if and only if v = 0 (mod 4). To prove that, some special sequences of integers are utilized. (C) 2002 Wiley Periodicals, Inc.
4-cycle group-divisible designs with two associate classes
(2001-07-01)
Fu, HL
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Rodger, CA
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應用數學系
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Department of Applied Mathematics
In this paper we investigate a partitioning problem, setting the existence problem for all group-divisible designs with first and second associates in which the blocks are 4-cycles.
A note on ascending subgraph decompositions of complete multipartite graphs
(2001-01-06)
Fu, HL
;
Hu, WH
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應用數學系
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Department of Applied Mathematics
In this note, we prove that the ascending subgraph decomposition conjecture is true for complete multipartite graphs. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: 05C70.
A novel use of t-packings to construct d-disjunct matrices
(2006-07-15)
Fu, HL
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Hwang, FK
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應用數學系
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Department of Applied Mathematics
A t-packing is an ordered pair (V, P) where V is a nu-set and P is a collection of k-subsets (blocks) of V such that each t-subset of V occurs in at most one block of P. If each t-subset of V occurs in exactly one block of P, then (V, P) is known as a Steiner (t, k, nu)-design. In this paper, we explore a novel use of t-packings to construct d-disjunct matrices. (c) 2006 Elsevier B.V. All rights reserved.
A resolvable r x c grid-block packing and its application to DNA library screening
(2004-12-01)
Mutoh, Y
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Jimbo, M
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Fu, HL
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應用數學系
;
Department of Applied Mathematics
For a nu-set V, let A be a collection of r x c arrays with elements in V. A pair (V, A) is called an r x c grid-block packing if every two distinct points i and j in V occur together at most once in the same row or in the same column of arrays in A. And an r x c grid-block packing (V, A) is said to be resolvable if the collection of arrays A can be partitioned into sub-classes R-1, R-2,..., R-t such that every point of V is contained in precisely one array of each class. These packings have originated from the use of DNA library screening. In this paper, we give some constructions of resolvable r x c grid-block packings and give a brief survey of their application to DNA library screening.
A solution to the forest leave problem for partial 6-cycle systems
(2004-04-28)
Ashe, DJ
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Fu, HL
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Rodger, CA
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應用數學系
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Department of Applied Mathematics
In this paper, we find necessary and sufficient conditions for the existence of a 6-cycle system of K-n - E(F) for every forest F of K-n. (C) 2003 Published by Elsevier B.V.
A study of the genus of a group
(2000-04-01)
Fu, HL
;
Sun, IF
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應用數學系
;
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 the total chromatic number of equibipartite graphs
(1998-04-06)
Chen, BL
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Cheng, CK
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Fu, HL
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Huang, KC
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應用數學系
The total chromatic number chi(t)(G) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same color, no incident edges receive the same color as either of the vertices it is incident with. In this paper, we obtain some results of the total chromatic number of the equibiparrite graphs of order 2n with maximum degree n - 1. As a part of our results, we disprove the biconformability conjecture. (C) 1998 Published by Elsevier Science B.V. All rights reserved.
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.
All 2-regular leaves of partial 6-cycle systems
(2005-07-01)
Ashe, DJ
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Rodger, CA
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Fu, HL
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應用數學系
;
Department of Applied Mathematics
In this paper, we find necessary and sufficient conditions for the exisience of a 6-cycle system of K-n - E(R) for every 2-regular not necessarily spanning subgraph R of K-n.
Almost Resolvable Directed m-cycle systems: m equivalent to 3 (mod 6)
(1999-10-01)
Fu, HL
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Rodger, CA
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應用數學系
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Department of Applied Mathematics
Let m = 3 (mod 6). We show there exists an almost resolvable directed m-cycle system of D-n if and only if n = 1 (mod m), except possibly if n is an element of {3m + 1, 6m + 1}.
Ascending subgraph decompositions of regular graphs
(2002-06-06)
Fu, HL
;
Hu, WH
;
應用數學系
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Department of Applied Mathematics
We prove that every regular graph with ((n+1)(2)) + t edges, 0 less than or equal to t < n + 1, can be decomposed into n subgraphs G(1),G(2),...,G(n) such that E(G(i)) = i and G(i) less than or equal to G(i+1) for i = 1,2,...,n - 1 and E(G(n)) = n + t. (C) 2002 Elsevier Science B.V. All rights reserved.
C-4-saturated bipartite graphs
(2002-12-28)
Bryant, DE
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Fu, HL
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應用數學系
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Department of Applied Mathematics
Let H be a graph. A graph G is said to be H-free if it contains no subgraph isomorphic to H. A graph G is said to be an H-saturated subgraph of a graph K if G is an H-free subgraph of K with the property that for any edge e is an element of E(K)E(G), G boolean OR {e} is not H-free. We present some general results on K-s,K-t-saturated subgraphs of the complete bipartite graph K-m,K-n and study the problem of finding, for all possible values of q, a C-4-saturated subgraph of K., having precisely q edges. (C) 2002 Elsevier Science B.V. All rights reserved.
Connectivity of cages
(1997-02-01)
Fu, HL
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Huang, KC
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Rodger, CA
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應用數學系
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Department of Applied Mathematics
A (k; g)-graph is a k-regular graph with girth g. Let f(k; g) be the smallest integer nu such there exists a (k; g)-graph with nu vertices. A (k; g)-cage is a (k; g)-graph with f(k; g) vertices. In this paper we prove that the cages are monotonic in that f(k; g(1)) < f(k; g(2)) for all k greater than or equal to 3 and 3 less than or equal to g(1) < g(2). We use this to prove that (k; g)-cages are 2-connected,and if k = 3 then their connectivity is k. (C) 1997 John Wiley & Sons, Inc.
Cyclic m-cycle systems with m <= 32 or m=2(q) with q a prime power
(2006-01-01)
Wu, SL
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Fu, HL
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應用數學系
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Department of Applied Mathematics
In this paper, the necessary and sufficient conditions for the existence of cyclic 2q-cycle and m-cycle systems of the complete graph with q a prime power and 3 <= m <= 32 are given. (c) 2005 Wiley Periodicals, Inc.
Cyclic m-cycle systems with m <= 32 or m=2q with q a prime power (vol 14, pg 66, 2005)
(2006-03-01)
Wu, SL
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Fu, HL
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應用數學系
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Department of Applied Mathematics
Cyclically decomposing the complete graph into cycles
(2004-05-06)
Fu, HL
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Wu, SL
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應用數學系
;
Department of Applied Mathematics
Let m(1), m(2),..., m(k) be positive integers not less than 3 and let n = Sigma(i=1)(k) m(i). Then, it is proved that the complete graph of order 2n + 1 can be cyclically decomposed into k(2n + 1) cycles such that, for each i = 1, 2,...,k, the cycle of length mi occurs exactly 2n + 1 times. (C) 2003 Elsevier B.V. All rights reserved.
Decomposing complete graphs into K-r x K-c's
(2004-02-01)
Fu, HL
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Hwang, FK
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Jimbo, M
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Mutoh, Y
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Shiue, CL
We consider the problem of decomposing a complete graph into the Cartesian product of two complete graphs K, and K, This problem originated from the clone library screening. We give a general method of constructing such decompositions using various sorts of combinatorial designs. In particular, for r = 3 and c = 3, we show that such a decomposition exists for all n satisfying some simple necessary conditions. (C) 2002 Elsevier B.V. All rights reserved.
Decomposing K-n UP into triangles
(2004-07-06)
Fu, CM
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Fu, HL
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Rodger, CA
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應用數學系
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Department of Applied Mathematics
In this paper, we extend the work on minimum coverings of K-n with triangles. We prove that when P is any forest on n vertices the multigraph G = K-n boolean OR P can be decomposed into triangles if and only if three trivial necessary conditions are satisfied: (i) each vertex in G has even degree, (ii) each vertex in P has odd degree, and (iii) the number of edges in G is a multiple of 3. This result is of particular interest because the corresponding packing problem where the leave is any forest is yet to be solved. We also consider some other families of packings, and provide a variation on a proof by Colbourn and Rosa which settled the packing problem when P is any 2-regular graph on at most n vertices. (C) 2004 Elsevier B.V. All rights reserved.
Embeddings of maximum packings in triple systems
(2004-07-06)
Su, RW
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Fu, HL
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Shen, H
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應用數學系
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Department of Applied Mathematics
Let MPT(v,lambda) denote a maximum packing of triples of order v with index lambda and TS(u, lambda) denote a triple system of order u with index lambda. For lambda > 1 and v greater than or equal to 6, it is proved in this paper that the necessary and sufficient conditions for the embedding of an MPT(v, lambda) in a TS(u, lambda) are lambda(u - 1) equivalent to 0 (mod 2), lambdau(u - 1) equivalent to 0 (mod 6) and u greater than or equal to 2v + 1. (C) 2003 Published by Elsevier B.V.