Abstract
In this paper, we introduce a simple scheme of generating ”good” bipartite graphs. A bipartite graph G with bipartition W and B is a good graph if it is 1-edge hamiltonian, 1(subscript p)-hamiltonian and hamiltonian laceable. More specifically, G is good if G-F remains hamiltonian where F consists of an edge or a pair of vertices {v1, v2|v1∈W, v2∈B}, and if there exists a hamiltonian path between u and v for any u∈W, v∈B. This scheme is called ”edge replacement”. Simple examples of good bipartite graphs, as well as the family of brother trees BT(n) with n≥1[4], are obtained as an application of edge replacement.
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