# Theory on Structure and Coloring of Maximal Planar Graphs (I): Relationship between Structure and Coloring

@article{Xu2012TheoryOS, title={Theory on Structure and Coloring of Maximal Planar Graphs (I): Relationship between Structure and Coloring}, author={Jin Xu}, journal={arXiv: General Mathematics}, year={2012} }

Maximal planar graph refers to the planar graph with the most edges, which means no more edges can be added so that the resulting graph is still planar. The Four-Color Conjecture says that every planar graph without loops is 4-colorable. Indeed, in order to prove Four-Color Conjecture, it clearly suffices to show that all maximal planar graphs are 4-colorable. Since this conjecture was proposed in 1852, no mathematical proofs have been invented up until now. Maybe the main reasons lie in the…

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