%0 Unpublished Work %1 cranston15 %A Cranston, Daniel W. %A Rabern, Landon %D 2015 %K graph.theory planar %T Planar Graphs are $9/2$-Colorable and Have Independence Ratio at Least $3/13$ %U http://arxiv.org/abs/1410.7233 %X We show that every planar graph G has a 2-fold 9-coloring. In particular, this implies that G has fractional chromatic number at most 92. This is the first proof (independent of the 4 Color Theorem) that there exists a constant k<5 such that every planar G has fractional chromatic number at most k. We also show that every n-vertex planar graph has an independent set of size at least 3n13. This improves on Albertson's bound of 2n9.

@unpublished{cranston15, abstract = {We show that every planar graph G has a 2-fold 9-coloring. In particular, this implies that G has fractional chromatic number at most 92. This is the first proof (independent of the 4 Color Theorem) that there exists a constant k<5 such that every planar G has fractional chromatic number at most k. We also show that every n-vertex planar graph has an independent set of size at least 3n13. This improves on Albertson's bound of 2n9.}, added-at = {2015-11-06T08:14:38.000+0100}, author = {Cranston, Daniel W. and Rabern, Landon}, biburl = {https://www.bibsonomy.org/bibtex/2b42dc512f8fcef4f8cd04264b31106b7/ytyoun}, interhash = {2e4d5fc19bf88aba73e73645a54af435}, intrahash = {b42dc512f8fcef4f8cd04264b31106b7}, keywords = {graph.theory planar}, timestamp = {2015-11-06T08:14:38.000+0100}, title = {Planar Graphs are $9/2$-Colorable and Have Independence Ratio at Least $3/13$}, url = {http://arxiv.org/abs/1410.7233}, year = 2015 }