Fractional Triangle Decompositions in Graphs with Large Minimum Degree

@article{Dross2016FractionalTD,
  title={Fractional Triangle Decompositions in Graphs with Large Minimum Degree},
  author={François Dross},
  journal={SIAM J. Discrete Math.},
  year={2016},
  volume={30},
  pages={36-42}
}
A triangle decomposition of a graph is a partition of its edges into triangles. A fractional triangle decomposition of a graph is an assignment of a nonnegative weight to each of its triangles such that the sum of the weights of the triangles containing any given edge is one. We prove that every graph on n vertices with minimum degree at least 0.9n has a fractional triangle decomposition. This improves a result of Garaschuk that the same conclusion holds for graphs with minimum degree at least… CONTINUE READING

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