Edge Disjoint Caterpillar Realizations
Abstract
In this paper, we consider the edge disjoint caterpillar realizations of tree degree sequences. We give the necessary and sufficient conditions when two tree degree sequences have edge disjoint caterpillar realizations. We conjecture that an arbitrary number of tree degree sequences have edge disjoint realizations if every vertex is a leaf in at most one tree. We prove that the conjecture is true if the number of tree degree sequences is at most $4$. We also prove that the conjecture is true if $n \ge \max\{22k11, 396\}$, where $n$ is the number of vertices and $k$ is the number of tree degree sequences.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.05986
 Bibcode:
 2019arXiv190505986M
 Keywords:

 Mathematics  Combinatorics