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Packing Three-Vertex Paths in a Subcubic Graph

Abstract : In our paper we consider the $P_3$-packing problem in subcubic graphs of different connectivity, improving earlier results of Kelmans and Mubayi. We show that there exists a $P_3$-packing of at least $\lceil 3n/4\rceil$ vertices in any connected subcubic graph of order $n>5$ and minimum vertex degree $\delta \geq 2$, and that this bound is tight. The proof is constructive and implied by a linear-time algorithm. We use this result to show that any $2$-connected cubic graph of order $n>8$ has a $P_3$-packing of at least $\lceil 7n/9 \rceil$ vertices.
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Adrian Kosowski, Michal Malafiejski, Pawel Zyliński. Packing Three-Vertex Paths in a Subcubic Graph. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.213-218. ⟨hal-01184370⟩

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