Monochromatic bounded degree subgraph partitions

@article{Grinshpun2016MonochromaticBD,
  title={Monochromatic bounded degree subgraph partitions},
  author={Andrey Grinshpun and G{\'a}bor N. S{\'a}rk{\"o}zy},
  journal={Discrete Mathematics},
  year={2016},
  volume={339},
  pages={46-53}
}
Let F = {F1, F2, . . .} be a sequence of graphs such that Fn is a graph on n vertices with maximum degree at most ∆. We show that there exists an absolute constant C such that the vertices of any 2-edge-colored complete graph can be partitioned into at most 2C∆log ∆ vertex disjoint monochromatic copies of graphs from F . If each Fn is bipartite, then we can improve this bound to 2C∆; this result is optimal up to the constant C.