On the Minimum EdgeDensity of 4Critical Graphs of Girth Five Academic Article uri icon

abstract

  • AbstractIn a recent seminal work, Kostochka and Yancey proved that for every 4critical graph G. In this article, we prove that for every 4critical graph G with girth at least five. When combined with another result of the second author, the improvement on the constant term leads to a corollary that there exist such that for every 4critical graph G with girth at least five. Moreover, it provides a unified and shorter proof of both a result of Thomassen and a result of Thomas and Walls without invoking any topological property, where the former proves that every graph with girth five embeddable in the projective plane or torus is 3colorable, and the latter proves the same for the Klein bottle.

published proceedings

  • Journal of Graph Theory

author list (cited authors)

  • Liu, C., & Postle, L.

citation count

  • 1

complete list of authors

  • Liu, Chun‐Hung||Postle, Luke

publication date

  • December 2017

publisher