Browsing by Author "Fu, H. L."

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Maximal sets of hamilton cycles in K(2p)-F
(2008-07-06)
Fu, H. L.
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Logan, S. L.
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Rodger, C. A.
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應用數學系
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Department of Applied Mathematics
A set S of edge-disjoint hamilton cycles in a graph T is said to be maximal if the hamilton cycles in S form a subgraph of T such that T - E(S) has no hamilton cycle. The spectrum of a graph T is the set of integers in such that T contains a maximal set of m edge-disjoint hamilton cycles. This spectrum has previously been determined for all complete graphs, all complete bipartite graphs, and many complete multipartite graphs. One of the outstanding problems is to find the spectrum for the graphs formed by removing the edges of a I-factor, F, from a complete graph, K(2p). In this paper we completely solve this problem, giving two substantially different proofs. One proof uses amalgamations, and is of interest in its own right because it is the first example of an amalgamation where vertices from different parts are amalgamated. The other is a neat direct proof. (c) 2007 Elsevier B.V. All rights reserved.
Multicolored parallelisms of isomorphic spanning trees
(2006)
Akbari, S.
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Alipour, A.
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Fu, H. L.
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Lo, Y. H.
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應用數學系
A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we prove that a complete graph on 2m (m not equal 2) vertices K-2m can be properly edge-colored with 2m - 1 colors in such a way that the edges of K-2m can be partitioned into m multicolored isomorphic spanning trees.
The minimum number of e-vertex-covers among hypergraphs with e edges of given ranks
(2009-01-06)
Chang, F. H.
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Fu, H. L.
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Hwang, F. K.
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Lin, B. C.
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應用數學系
We study the problem that among all hypergraphs with e edges of ranks l(1), ..., l(e) an v vertices, which hypergraph has the least number of vertex-covers of size e. The problem is very difficult and we only get some partial answers. We show an application of our results to improve the error-tolerance of a pooling design proposed in the literature. (c) 2008 Elsevier B.V. All rights reserved.