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
1 Citations
Minimum maximal matchings in cubic graphs

References

SHOWING 1-10 OF 22 REFERENCES
Bipartite density and the independence ratio
  • S. C. Locke
  • Mathematics, Computer Science
  • J. Graph Theory
  • 1986
Independent sets in triangle-free cubic planar graphs
11/30 (Finding Large Independent Sets in Connected Triangle-Free 3-Regular Graphs)
A new proof of the independence ratio of triangle-free cubic graphs
On the independence number of triangle free graphs with maximum degree three
  • Journal of Combinatorial Mathematics and Combinatorial Computing,
  • 1998
On the independence number of triangle free graphs with maximum degree three
  • Journal of Combinatorial Mathematics and Combinatorial Computing,
  • 1998
Some Ramsey-type numbers and the independence ratio
Cubic Graphs with Small Independence Ratio
Fractional chromatic number, maximum degree and girth
Independent sets and cuts in large-girth regular graphs
  • E. Csóka
  • Computer Science, Mathematics
  • ArXiv
  • 2016
...
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2
3
...