Geodesic
The Grötzsch theorem for the hypergraph of maximal cliques
The electronic journal of combinatorics, Tome 6 (1999)
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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
Classification : 05C15, 05C65, 05C69
Mots-clés : clique hypergraph, monochromatic, planar graph, list colorings 
@article{10_37236_1458,
     author = {Bojan Mohar and Riste Skrekovski},
     title = {The {Gr\"otzsch} theorem for the hypergraph of maximal cliques},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1458},
     zbl = {0930.05040},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1458/}
}
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Bojan Mohar; Riste Skrekovski. The Grötzsch theorem for the hypergraph of maximal cliques. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1458

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