Browsing by Author "Rodger, C. A."

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All graphs with maximum degree three whose complements have 4-cycle decompositions
(2008-07-06)
Fu, Chin-Mei
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Fu, Hung-Lin
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Rodger, C. A.
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Smith, Todd
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應用數學系
Let g be the set that contains precisely the graphs on n vertices with maximum degree 3 for which there exists a 4-cycle system of their complement in K(n). In this paper g is completely characterized. (C) 2007 Elsevier B.V. All rights reserved.
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.
On the number of rainbow spanning trees in edge-colored complete graphs
(2018-08-01)
Fu, Hung-Lin
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Lo, Yuan-Hsun
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Perry, K. E.
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Rodger, C. A.
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應用數學系
A spanning tree of a properly edge-colored complete graph, K, is rainbow provided that each of its edges receives a distinct color. In 1996, Brualdi and Hollingsworth conjectured that if K-2m is properly (2m 1)-edge-colored, then the edges of K-2m,, can be partitioned into m rainbow spanning trees except when m = 2. By means of an explicit, constructive approach, in this paper we construct [root 6m+9/3] mutually edge-disjoint rainbow spanning trees for any positive value of m. Not only are the rainbow trees produced, but also some structure of each rainbow spanning tree is determined in the process. This improves upon best constructive result to date in the literature which produces exactly three rainbow trees. (C) 2018 Elsevier B.V. All rights reserved.