# Vertex-Disjoint Cycles of Order Eight with Chords in a Bipartite Graph

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Let $$K$$ be a set of $$k$$ positive integers. A biclique cover of type $$K$$ of a graph $$G$$ is a collection of complete bipartite subgraphs of $$G$$ such that for every edge $$e$$ of $$G$$ , the number of bicliques need to cover $$e$$ is a member of $$K$$ . If $$K=\{1,2,\ldots , k\}$$ then...

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A basis B for the cycle space C(G) of a graph G is called a d-fold if each edge of G occurs in at most d of the cycles in the basis B. A basis B for the cycle space C(G) of a graph G is Smarandachely if each edge of G occurs in at least 2 of the cycles in B. The basis number, b(G), of a graph G...

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In path factorization, Ushio [1] gave the necessary and sufficient conditions for Pk-design when k is odd. P2p-factorization of a complete bipartite graph for p an integer, was studied by Wang [2]. Further, Beiling [3] extended the work of Wang [2], and studied P2k-factorization of complete...