一种特殊的多米诺扩缩运算

刘小青; 许进

doi:10.11999/JEIT160886

一种特殊的多米诺扩缩运算

doi: 10.11999/JEIT160886

刘小青¹,
许进^1,

基金项目:

国家973计划项目(2013CB329600)，国家自然科学基金(61372191, 61472012, 61472433, 61572046, 61502012, 61572492, 61572153, 61402437)

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- 文章访问数: 1072
- HTML全文浏览量: 110
- PDF下载量: 329
- 被引次数: 0
出版历程
- 收稿日期: 2016-08-29
- 修回日期: 2016-12-06
- 刊出日期: 2017-01-19

Special Type of Domino Extending-contracting Operations

LIU Xiaoqing¹,
XU Jin^1
,

Funds:

The National 973 Program of China (2013CB329600), The National Natural Science Foundation of China (61372191, 61472012, 61472433, 61572046, 61502012, 61572492, 61572153, 61402437)

摘要

摘要: 该文提出一种称为334扩缩运算的多米诺扩缩运算。使用该运算构造了一类特殊的极大平面图334-型极大平面图，证明了该类图均为树型2-色不变圈着色，且每个4k -阶334-型极大平面图恰有2k-1个2-色不变圈着色及2k-2个树着色。证明了该运算可用于构造纯树着色极大平面图，并提出猜想：若极大平面图G是纯树(纯圈，混合)着色，则对G实施334扩(缩)轮运算后，所得之图仍是纯树(纯圈，混合)着色。
- 半封漏斗 /
- 树型2-色不变圈着色 /
- 纯树着色 /
- 334扩轮运算
Abstract: In this paper, a new domino extending-contracting operation, called 334 extending-contracting operation, is put forward, on the basis of which, it is proposed to construct a particular kind of graphs, i.e., 334-type maximal planar graphs, and proved that all those graphs are tree-type and 2-chromatic cycle-unchanged colored and every 334-type maximal planar graphs of order4k has exactly2k-1 2-chromatic cycled-unchanged colorings and2k-2 tree-colorings. Additionally, it is proved that an infinite family of purely tree-colored graphs can be generated by implementing a series of 334 extending-wheel operations, and conjectured that if a maximal planar graph Gis purely tree-colored (purely cycle-colored or impure-colored), then the graph obtained by implementing one 334 extending-wheel (contracting-wheel) operation on G is still purely tree-colored (purely cycle-colored or impure-colored).
- Semi-funnels /
- Tree-type and 2-chromatic cycle-unchanged colored /
- Purely tree-colored /
- 334 extending- wheel operations

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参考文献(18)

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