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Hamilton-connected properties in cartesian productKeywords: Cartesian product , Hamilton-connectedness , Hamilton cycle , Hamilton path Abstract: In this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. We present some sufficient and necessary conditions for $GBox H$ being hamilton-connected when $G$ is a hamilton-connected graph and $H$ is a tree or $G$ is a hamiltonian graph and $H$ is $K_2$.
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