The Grötzsch Theorem for the Hypergraph of Maximal Cliques

Bojan Mohar, Riste Skrekovski
1999 Electronic Journal of Combinatorics  
In this paper, we extend the Grötzsch Theorem by proving that the clique hypergraph ${\cal H}(G)$ of every planar graph is 3-colorable. We also extend this result to list colorings by proving that ${\cal H}(G)$ is 4-choosable for every planar or projective planar graph $G$. Finally, 4-choosability of ${\cal H}(G)$ is established for the class of locally planar graphs on arbitrary surfaces.
doi:10.37236/1458 fatcat:mk3jt7rwfzdbpnkte4uya34na4