# Large independent sets in triangle-free cubic graphs: beyond planarity

@article{Batenburg2019LargeIS, title={Large independent sets in triangle-free cubic graphs: beyond planarity}, author={W. C. V. Batenburg and Jan Goedgebeur and G. Joret}, journal={ArXiv}, year={2019}, volume={abs/1911.12471} }

The _independence ratio_ of a graph is the ratio of the size of its largest independent set to its number of vertices. Trivially, the independence ratio of a k-colorable graph is at least $1/k$ as each color class of a k-coloring is an independent set. However, better bounds can often be obtained for well-structured classes of graphs. In particular, Albertson, Bollobas and Tucker conjectured in 1976 that the independence ratio of every triangle-free subcubic planar graph is at least $3/8$. The… Expand

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