Partitioning Graphs Into Paths or Cycles of Prescribed Lengths
Journal of Combinatorics
In this paper, we consider the path (and cycle) partition problem for graphs with additional length restrictions. More specifically, we prove sufficient degree sum conditions for the vertices of a graph to be partitioned into paths, with fixed end vertices, such that these paths have approximately prescribed lengths. We also prove similar results for partitions into cycles of approximately prescribed lengths each containing a specified vertex.
Magnant, Colton, Kenta Ozeki.
"Partitioning Graphs Into Paths or Cycles of Prescribed Lengths."
Journal of Combinatorics, 3 (2): 135-161.