Browsing by Author "Rodger, CA"

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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 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.
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
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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}.
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.
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.
Forest leaves and four-cycles
(2000-03-01)
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 article, we find necessary and sufficient conditions for the existence of a 4-cycle system of K-n - E(F) for any forest F of K-n. (C) 2000 John Wiley & Sons, Inc.
Four-cycle systems with two-regular leaves
(2001)
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 settle the existence problem for 4-cycle systems of K-n - E(F) and of 2K(n) - E(F) for all 2-regular subgraphs F.
Group divisible designs with two associate grasses: n=2 or m=2
(1998-07-01)
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 ive iind necessary and sufficient conditions For the existence of a group divisible design GDD(n, m) of index (lambda(1), lambda(2)) in which n = 2 or m = 2, thereby completing the solution of the existence problem for all n, m, lambda(1), and lambda(2). In the process. necessary and sufficient conditions are found For the existence of an x-regular partial triple system whose complement in lambda K-n has a 1-factorization. (C) 1998 Academic Press.
Packing complete multipartite graphs with 4-cycles
(2001)
Billington, EJ
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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 completely solve the problem of finding a maximum packing of any complete multipartite graph with edge-disjoint 4-cycles, and the minimum leaves are explicitly given. (C) 2001 John Wiley & Sons, Inc.
Packing lambda-fold complete multipartite graphs with 4-cycles
(2005-06-01)
Billington, EJ
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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
A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.
The Doyen-Wilson theorem for minimum coverings with triples
(1997-01-01)
Fu, HL
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Lindner, CC
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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 article necessary and sufficient conditions are found for a minimum covering of K-m with triples to be embedded in a minimum covering of K-n with triples. (C) 1997 John Wiley & Sons, Inc.
The Doyen-Wilson theorem for minimum coverings with triples
(1997-01-01)
Fu, HL
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Lindner, CC
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Rodger, CA
;
應用數學系
;
Department of Applied Mathematics
In this article necessary and sufficient conditions are found for a minimum covering of K-m with triples to be embedded in a minimum covering of K-n with triples. (C) 1997 John Wiley & Sons, Inc.
The existence of group divisible designs with first and second associates, having block size 3
(2000-01-01)
Fu, HL
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Rodger, CA
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Sarvate, DG
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應用數學系
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Department of Applied Mathematics
We completely settle the existence problem for group divisible designs with first and second associates in which the block size is 3, and with m groups each of size n, where n, m greater than or equal to 3.
The minimum size of critical sets in latin squares
(1997-08-15)
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
A critical set C of order n is a partial latin square of order n which is uniquely completable to a latin square, and omitting any entry of the partial latin square destroys this property. The size s(C) of a critical set C is the number of filled cells in the partial latin square. The size of a minimum critical set of order n is s(n). It is likely that s(n) is approximately 1/4n(2), though to date the best-known lower bound is that s(n)greater than or equal to n+1. In this paper, we obtain some conditions on C which force s(C)greater than or equal to[(n-1)/2](2). For n > 20, this is used to show that in generals(n)greater than or equal to[(7n-3)/6], thus improving the best-known result. (C) 1997 Elsevier Science B.V.
The minimum size of critical sets in latin squares
(1997-08-15)
Fu, CM
;
Fu, HL
;
Rodger, CA
;
應用數學系
;
Department of Applied Mathematics
A critical set C of order n is a partial latin square of order n which is uniquely completable to a latin square, and omitting any entry of the partial latin square destroys this property. The size s(C) of a critical set C is the number of filled cells in the partial latin square. The size of a minimum critical set of order n is s(n). It is likely that s(n) is approximately 1/4n(2), though to date the best-known lower bound is that s(n)greater than or equal to n+1. In this paper, we obtain some conditions on C which force s(C)greater than or equal to[(n-1)/2](2). For n > 20, this is used to show that in generals(n)greater than or equal to[(7n-3)/6], thus improving the best-known result. (C) 1997 Elsevier Science B.V.
Two Doyen-Wilson theorems for maximum packings with triples
(1998-01-01)
Fu, HL
;
Lindner, CC
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Rodger, CA
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應用數學系
;
Department of Applied Mathematics
In this paper we complete the work begun by Mendelsohn and Rosa and by Hartman, finding necessary and sufficient conditions for a maximum packing with triples of order m MPT(m) to be embedded in an MPT(n). We also characterize when it is possible to embed an MPT(m) with leave L-1 in an MPT(n) with leave L-2 in such a way that L-1 subset of or equal to L-2.