Theory on Structure and Coloring of Maximal Planar Graphs (3) Purely Tree-colorable and Uniquely 4-colorable Maximal Planar Graph Conjectures

XU Jin

doi:10.11999/JEIT160409

Volume 38 Issue 6

Jun. 2016

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Article Navigation > Journal of Electronics & Information Technology > 2016 > 38(6): 1328-1353

XU Jin. Theory on Structure and Coloring of Maximal Planar Graphs (3) Purely Tree-colorable and Uniquely 4-colorable Maximal Planar Graph Conjectures[J]. Journal of Electronics & Information Technology, 2016, 38(6): 1328-1353. doi: 10.11999/JEIT160409

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XU Jin. Theory on Structure and Coloring of Maximal Planar Graphs (3) Purely Tree-colorable and Uniquely 4-colorable Maximal Planar Graph Conjectures[J]. Journal of Electronics & Information Technology, 2016, 38(6): 1328-1353. doi: 10.11999/JEIT160409

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Theory on Structure and Coloring of Maximal Planar Graphs (3) Purely Tree-colorable and Uniquely 4-colorable Maximal Planar Graph Conjectures

doi: 10.11999/JEIT160409 cstr: 32379.14.JEIT160409

XU Jin¹

Funds:

The National 973 Program of China (2013CB 329600), The National Natural Science Foundation of China (61372191, 61472012, 61472433, 61572046, 61502012, 61572492, 61572153, 61402437)

Received Date: 2016-04-22
Rev Recd Date: 2016-04-26
Publish Date: 2016-06-19

Abstract

Abstract

A maximal planar graph is called the recursive maximal planar graph if it can be obtained fromK4 by embedding a 3-degree vertex in some triangular face continuously. The uniquely 4-colorable maximal planar graph conjecture states that a planar graph is uniquely 4-colorable if and only if it is a recursive maximal planar graph. This conjecture, which has 43 years of history, is a very influential conjecture in graph coloring theory after the Four-Color Conjecture. In this paper, the structures and properties of dumbbell maximal planar graphs and recursive maximal planar graphs are studied, and an idea of proving the uniquely 4-colorable maximal planar graph conjecture is proposed based on the extending-contracting operation proposed in this series of article (2).

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References(43)

References

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