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Packing Three-Vertex Paths in a Subcubic Graph

By Adrian Kosowski and et al. Michał Małafiejski


In our paper we consider the P3-packing problem in subcubic graphs of different connectivity, improving earlier results of Kelmans and Mubayi (5). We show that there exists a P3-packing of at least ⌈3n/4 ⌉ vertices in any connected subcubic graph of order n> 5 and minimum vertex degree δ ≥ 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 P3-packing of at least ⌈7n/9 ⌉ vertices

Topics: three-vertex paths, subcubic graphs, path packing
Year: 2005
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