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A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order n ≥ 9 and size at least 7n−13 2 contains two disjoint theta graphs. We also show that every 2-edge-connected graph of order n ≥ 6 and size at least 3n − 5 contains two disjoint cycles, such that any specified vertex(More)
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