Browsing by Author "Huang, Ming-Hway"

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(4,5)-CYCLE SYSTEMS OF COMPLETE MULTIPARTITE GRAPHS
(2012-06-01)
Huang, Ming-Hway
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
In 1981, Alspach conjectured that if 3 <= m(i) <= v, v is odd and v(v - 1)/2 = m(1) +m(2)+ ... +m(t) then the complete graph K-v can be decomposed into t cycles of lengths m(1), m(2), ... , m(t) respectively; if v is even, v(v - 2)/2 = m(1) + m(2) ... + m(t), then the complete graph minus a one-factor K-v - F can be decomposed into t cycles of lengths m(1), m(2),..., Tat respectively. In this paper, we extend the study to the decomposition of the complete equipartite graph K-m(n).For m(i) is an element of {4, 5}, we prove that the trivial necessary conditions are also sufficient.
"(4,5)-CYCLE SYSTEMS OF COMPLETE MULTIPARTITE GRAPHS"
(2012-06-01)
Huang, Ming-Hway
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
"In 1981, Alspach conjectured that if 3 <= m(i) <= v, v is odd and v(v - 1)/2 = m(1) +m(2)+ ... +m(t) then the complete graph K-v can be decomposed into t cycles of lengths m(1), m(2), ... , m(t) respectively; if v is even, v(v - 2)/2 = m(1) + m(2) ... + m(t), then the complete graph minus a one-factor K-v - F can be decomposed into t cycles of lengths m(1), m(2),..., Tat respectively. In this paper, we extend the study to the decomposition of the complete equipartite graph K-m(n).For m(i) is an element of {4, 5}, we prove that the trivial necessary conditions are also sufficient."
Packing 5-cycles into balanced complete m-partite graphs for odd m
(2007-10-01)
Huang, Ming-Hway
;
Fu, Chin-Mei
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
Let K-n1,(n2),..., n(m) be a complete m-partite graph with partite sets of sizes n(1),n(2),...,n(m). A complete m-partite graph is balanced if each partite set has n vertices. We denote this complete m-partite graph by K-m(n). In this paper, we completely solve the problem of finding a maximum packing of the balanced complete m-partite graph K-m(n), m odd, with edge-disjoint 5-cycles and we explicitly give the minimum leaves.