All Planar Graphs are 5-colorable, Complete Proof: https://www.whitman.edu/mathematics/cgt_online/book/section05.10.html

All Planar Graphs are 4-colorable, sketch from wikipedia https://en.wikipedia.org/wiki/Four_color_theorem

Fractional graph Theory by by Scheinerman and Ullman. This is a book. https://www.ams.jhu.edu/ers/wp-content/uploads/sites/2/2015/12/fgt.pdf

Planar Graphs are 4.5 colorable and have ind ratio at least 0.3… By Cranston and Raybern paper talk