For sufficiently large connected graphs, minimum degree at least h forces any fixed linear forest with at most two odd paths, except for explicit families of graphs.
Gorgol, Tur\' a n number for disjoint copies of graphs, Graphs Combin
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Erdos-Gallai Stability Theorem for Linear Forests
For sufficiently large connected graphs, minimum degree at least h forces any fixed linear forest with at most two odd paths, except for explicit families of graphs.