Theory on Structure and Coloring of Maximal Planar Graphs (2) Domino Configurations and Extending-Contracting Operations

XU Jin

doi:10.11999/JEIT160224

Volume 38 Issue 6

Jun. 2016

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Article Navigation > Journal of Electronics & Information Technology > 2016 > 38(6): 1271-1327

XU Jin. Theory on Structure and Coloring of Maximal Planar Graphs (2) Domino Configurations and Extending-Contracting Operations[J]. Journal of Electronics & Information Technology, 2016, 38(6): 1271-1327. doi: 10.11999/JEIT160224

Citation:

XU Jin. Theory on Structure and Coloring of Maximal Planar Graphs (2) Domino Configurations and Extending-Contracting Operations[J]. Journal of Electronics & Information Technology, 2016, 38(6): 1271-1327. doi: 10.11999/JEIT160224

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Theory on Structure and Coloring of Maximal Planar Graphs (2) Domino Configurations and Extending-Contracting Operations

doi: 10.11999/JEIT160224

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: 2016-01-24
Rev Recd Date: 2016-04-21
Publish Date: 2016-06-19

Abstract

Abstract

The first paper of this series of articles revealed that Four-Color Conjecture is hopefully proved mathematically by investigating a special class of graphs, called the 4-chromatic-funnel, pseudo uniquely-4- colorable maximal planar graphs. To characterize the properties of such class of graphs, a novel technique, extending-contracting operation, is proposed which can be used to construct maximal planar graphs. The essence of this technique is to study a special kind of configurations, domino configurations. In this paper, a necessary and sufficient condition for a planar graph to be a domino configuration is constructively given, on the basis of which it is proposed to construct the ancestor-graphs and descendent-graphs of a graph. Particularly, it is proved that every maximal planar graph with ordern(9) and minimum degree4 has an ancestor-graph of order(n-2) or (n-3). Moreover, an approach is put forward to construct maximal planar graphs recursively, by which all maximal planar graphs with order 6~12 and minimum degree 4 are constructed. The extending-contracting operation constitutes the foundation in this series of articles.
- Maximal planar graphs,
- Extending-contracting operations,
- Domino configurations,
- Ancestor-graphs,
- Descendent-graphs,
- Recursive construction approach

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References(26)

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