Decomposing Cubic Graphs into Connected Subgraphs of Size Three

Abstract : Let S = {K1,3, K3, P4} be the set of connected graphs of size 3. We study the problem of partitioning the edge set of a graph G into graphs taken from any non-empty S ⊆ S. The problem is known to be NP-complete for any possible choice of S in general graphs. In this paper, we assume that the input graph is cubic, and study the computational complexity of the problem of partitioning its edge set for any choice of S. We identify all polynomial and NP-complete problems in that setting, and give graph-theoretic characterisations of S-decomposable cubic graphs in some cases.
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Laurent Bulteau, Guillaume Fertin, Anthony Labarre, Romeo Rizzi, Irena Rusu. Decomposing Cubic Graphs into Connected Subgraphs of Size Three. The 22nd International Computing and Combinatorics Conference (COCOON), Aug 2016, Ho Chi Minh City, Vietnam. ⟨hal-01309152⟩

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