Browsing by Author "Bryant, DE"

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C-4-saturated bipartite graphs
(2002-12-28)
Bryant, DE
;
Fu, HL
;
應用數學系
;
Department of Applied Mathematics
Let H be a graph. A graph G is said to be H-free if it contains no subgraph isomorphic to H. A graph G is said to be an H-saturated subgraph of a graph K if G is an H-free subgraph of K with the property that for any edge e is an element of E(K)E(G), G boolean OR {e} is not H-free. We present some general results on K-s,K-t-saturated subgraphs of the complete bipartite graph K-m,K-n and study the problem of finding, for all possible values of q, a C-4-saturated subgraph of K., having precisely q edges. (C) 2002 Elsevier Science B.V. All rights reserved.
(m,n)-cycle systems
(1998-11-01)
Bryant, DE
;
Khodkar, A
;
Fu, HL
;
應用數學系
;
Department of Applied Mathematics
We describe a method which, in certain circumstances, may be used to prove that the well-known necessary conditions for partitioning the edge set of the complete graph on an odd number of vertices (or the complete graph on an even number of vertices with a 1-factor removed) into cycles of lengths m(1),m(2),...,m(t) are sufficient in the case {m(1), m(2), ..., m(t)}=2. The method is used to settle the case where the cycle lengths are 4 and 5. (C) 1998 Elsevier Science B.V. All rights reserved.
(m,n)-cycle systems
(1998-11-01)
Bryant, DE
;
Khodkar, A
;
Fu, HL
;
應用數學系
;
Department of Applied Mathematics
We describe a method which, in certain circumstances, may be used to prove that the well-known necessary conditions for partitioning the edge set of the complete graph on an odd number of vertices (or the complete graph on an even number of vertices with a 1-factor removed) into cycles of lengths m(1),m(2),...,m(t) are sufficient in the case \{m(1), m(2), ..., m(t)}\=2. The method is used to settle the case where the cycle lengths are 4 and 5. (C) 1998 Elsevier Science B.V. All rights reserved.