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In this paper, we consider the edge disjoint caterpillar realizations of treedegree sequences. We give the necessary and sufficient conditions when two treedegree sequences have edge disjoint caterpillar realizations. We conjecturethat an arbitrary number of tree degree sequences have edge disjointrealizations if every vertex is a leaf in at most one tree. We prove that theconjecture is true if the number of tree degree sequences is at most $4$. Wealso prove that the conjecture is true if $n \ge \max\{22k-11, 396\}$, where$n$ is the number of vertices and $k$ is the number of tree degree sequences.

Edge Disjoint Caterpillar Realizations