| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 94 === Let G0 = (V0, E0) and G1 = (V1, E1) be two graphs such that |V0| = |V1| = t. Let M be an arbitrary perfect matching between G0 and G1. More specifically, M is a set of t edges with one endpoint in G0 and the other in G1. Define G = G(G0, G1; M) such that V(G) = V0 union V1 and E(G) = E0 union E1 union M. In this artical, we prove that when G0 and G1 are two bipartite hamiltonian laceable graphs, then G is hamiltonian laceable if G is a bipartite graph, and it is hamiltonian connected if G is a nonbipartite graph. When G0 and G1 are
two nonbipartite hamiltonian connected graphs, G is hamiltonian connected. When G0 is a bipartite hamiltonian laceable graph and G1 is a nonbipartite hamiltonian connected graph, G is hamiltonian connected. When G0, G1 are two graphs that are bipartite, hamiltonian laceable and bipancyclic, G is bipancyclic if G is a bipartite graph. When G0, G1 be two graphs that are hamiltonian connected and pancyclic, G contains cycles with length n for 3 < = n < = 2t, n not equal to t+1.When G0 is a bipartite graph that is hamiltonian laceable and bipancyclic,G1 ia a hamiltonian connected and pancyclic graph, G contains cycles with length n for 3 < = n < =2t, n not equal to t+1. When G0 and G1 are bipartite and bipanconnected graph and G is a nonbipartite graph.
Let H ={ {x,y} is a subset of V(G0)|(x,y) belong to E(G0) x bar , y bar belong to the same partition of G1}.Let d*= min{d{G1}( a bar ,b bar)| {a,b} belong to H }. Then G contains cycles of length l for any odd integer l with d*+3 < = l < = |G0|+|G1|- 1. When G0 and G1 are two graphs that are bipartite and hamiltonian laceable,G is bi-globally-3*-connected if G is a bipartite graph and it is globally-3*-connected if G is a nonbipartite graph. When G0 and G1 are two hamiltonian connected graphs, G is globally-3*-connected. When G0 is a bipartite hamiltonian laceable graph and G1 is a nonbipartite hamiltonian connected graph, G is globally-3*-connected.
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