Partitioning Sparse Graphs into an Independent Set and a Forest of Bounded Degree

نویسندگان

  • François Dross
  • Mickaël Montassier
  • Alexandre Pinlou
چکیده

An (I,Fd)-partition of a graph is a partition of the vertices of the graph into two sets I and F , such that I is an independent set and F induces a forest of maximum degree at most d. We show that for all M < 3 and d ≥ 2 3−M − 2, if a graph has maximum average degree less than M , then it has an (I,Fd)-partition. Additionally, we prove that for all 8 3 ≤ M < 3 and d ≥ 1 3−M , if a graph has maximum average degree less than M then it has an (I,Fd)-partition.

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عنوان ژورنال:
  • Electr. J. Comb.

دوره 25  شماره 

صفحات  -

تاریخ انتشار 2018