• Corpus ID: 96463185

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

  title={Theory on Structure and Coloring of Maximal Planar Graphs (I): Relationship between Structure and Coloring},
  author={Jin Xu},
  journal={arXiv: General Mathematics},
  • Jin Xu
  • Published 16 October 2012
  • Mathematics
  • arXiv: General Mathematics
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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