Browsing by Author "Wu, Shung-Liang"

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A note on cyclic m-cycle systems of K-r((m))
(2006-11-01)
Wu, Shung-Liang
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
It was proved by Buratti and Del Fra that for each pair of odd integers r and m, there exists a cyclic m-cycle system of the balanced complete r-partite graph K-r(m) except for the case when r=m=3. In this note, we study the existence of a cyclic m-cycle system of K-r(m) where r or m is even. Combining the work of Buratti and Del Fra, we prove that cyclic m-cycle systems of K-r(m) exist if and only if (a) K-r(m) is an even graph (b) (r, m) not equal (3, 3) and (c) (r,m) not equivalent to (t , 2) (mod 4) where t is an element of {2,3}.
Maximum cyclic 4-cycle packings of the complete multipartite graph
(2007-10-01)
Wu, Shung-Liang
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
A graph G is said to be m-sufficient if m is not exceeding the order of G, each vertex of G is of even degree, and the number of edges in G is a multiple of m. A complete multipartite graph is balanced if each of its partite sets has the same size. In this paper it is proved that the complete multipartite graph G can be decomposed into 4-cycles cyclically if and only if G is balanced and 4-sufficient. Moreover, the problem of finding a maximum cyclic packing of the complete multipartite graph with 4-cycles are also presented.