Browsing by Author "Shen, Hao"

Now showing 1 - 7 of 7

(C)over-right-arrow(4)-decompositions of D-v\P and D-v boolean OR P where P is a 2-regular subgraph of D-v
(2006-12-01)
Pu, Liqun
;
Fu, Hung-Lin
;
Shen, Hao
;
應用數學系
;
Department of Applied Mathematics
In this paper, we extend the study of C-4-decompositions of the complete graph with 2-regular leaves and paddings to directed versions. Mainly, we prove that if P is a vertex-disjoint union of directed cycles in a complete digraph D-v, then D-v\P and D-v boolean OR Pcan be decomposed into directed 4-cycles, respectively, if and only if v(v-1) - vertical bar E(P)vertical bar = 0 (mod 4) and v(v-1) + vertical bar E(P)vertical bar = 0 (mod 4) where vertical bar E(P)vertical bar denotes the number of directed edges of P, and v >= 8.
(C)over-right-arrow(4)-decompositions of D-vP and D-v boolean OR P where P is a 2-regular subgraph of D-v
(2006-12-01)
Pu, Liqun
;
Fu, Hung-Lin
;
Shen, Hao
;
應用數學系
;
Department of Applied Mathematics
In this paper, we extend the study of C-4-decompositions of the complete graph with 2-regular leaves and paddings to directed versions. Mainly, we prove that if P is a vertex-disjoint union of directed cycles in a complete digraph D-v, then D-vP and D-v boolean OR Pcan be decomposed into directed 4-cycles, respectively, if and only if v(v-1) - vertical bar E(P)vertical bar = 0 (mod 4) and v(v-1) + vertical bar E(P)vertical bar = 0 (mod 4) where vertical bar E(P)vertical bar denotes the number of directed edges of P, and v >= 8.
Directed 3-cycle decompositions of complete directed graphs with quadratic leaves
(2009-07-28)
Pu, Liqun
;
Fu, Hung-Lin
;
Shen, Hao
;
應用數學系
;
Department of Applied Mathematics
Let G be a vertex-disjoint union of directed cycles in the complete directed graph D(t), let vertical bar E(G)vertical bar be the number of directed edges of G and suppose G not equal 54 (C) over right arrow (2) boolean OR (C) over right arrow (3) or (C) over right arrow (5) if t = 5, and G not equal (C) over right arrow (3) boolean OR (C) over right arrow (3) if t = 6. It is proved in this paper that for each positive integer t, there exist (C) over right arrow (3)-decompositions for D(t) - G if and only if t(t - 1) -vertical bar E(G)vertical bar equivalent to 0 (mod 3). (C) 2008 Elsevier B.V. All rights reserved.
Maximal sets of Hamilton cycles in Dn
(2008-08-28)
Pu, Liqun
;
Fu, Hung-Lin
;
Shen, Hao
;
應用數學系
;
Department of Applied Mathematics
In this paper, we prove that there exists a maximal set of in directed Hamilton cycles in D(n) if and only if [n/2] <= m <= n -1 for n >= 7. (C) 2007 Elsevier B.V. All rights reserved.
Maximum Packing of Dt-P and Dt boolean OR P with Mendelsohn Triples
(2009-04-01)
Pu, Liqun
;
Fu, Hung-Lin
;
Shen, Hao
;
應用數學系
;
Department of Applied Mathematics
In this paper, we extend the study on packing and covering of complete directed graph D(t) with Mendelsohn triples [6]. Mainly, the maximum packing of D(t) - P and D(t) boolean OR P with Mendelsohn triples are obtained respectively where P is a vertex-disjoint union of directed cycles in D(t).
The Hamilton-Waterloo problem for Hamilton cycles and C(4k)-factors
(2011-07-01)
Lei, Hongchuan
;
Fu, Hung-Lin
;
Shen, Hao
;
應用數學系
;
Department of Applied Mathematics
In this paper we give a complete solution to the Hamilton-Waterloo problem for the case of Hamilton cycles and C(4k)-factors for all positive integers k.
The Hamilton-Waterloo problem for Hamilton cycles and C-4k-factors
(2011-07-01)
Lei, Hongchuan
;
Fu, Hung-Lin
;
Shen, Hao
;
應用數學系
;
Department of Applied Mathematics
In this paper we give a complete solution to the Hamilton-Waterloo problem for the case of Hamilton cycles and C-4k-factors for all positive integers k.