Graphs & digraphs (2nd ed.)
Path factors of bipartite graphs
Journal of Graph Theory
The Pk Partition Problem and Related Problems in Bipartite Graphs
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Packing 3-vertex paths in claw-free graphs and related topics
Discrete Applied Mathematics
The path partition problem and related problems in bipartite graphs
Operations Research Letters
Packing paths: Recycling saves time
Discrete Applied Mathematics
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A P≥3-factor F of a graph G is a spanning subgraph of G such that every component of F is a path of length at least two. Let R be a factor-critical graph with at least three vertices, that is, for each x ∈ V(R), R - x has a 1-factor (i.e., a perfect matching). Set V(R) = {x1, ...,xn}. Add new vertices {v1, ..., vn} to R together with the edges xivi, 1 ≤ i ≤ n. The resulting graph H is called a sun. (Note that degH vi = 1 for all i, 1≤i≤n.) K1 and K2, i.e., the complete graphs with one and two vertices, respectively, are also called suns. Then let C be the set of all suns. A sun component of a graph is a component which belongs to C. Let cs(G) denote the number of sun components of G. We prove that a graph G has a P≥3-factor if and only if cs(G - S)≤2|S|, for every subset S of V(G).