在可以嵌入到超立方体层中的图形上,以及它们的极限数
Maria Axenovich1, Ryan R Martin2, Christian Winter1
1Karlsruhe Institute of Technology, Karlsruhe, Germany.
概括
这项研究研究了立方图及其在超立方体中的图兰密度. 我们描述了分层图形,并表明大多数分区的图兰密度为零,但一些非分层图形的密度为正.
科学领域:
- 图形理论是指图形的理论.
- 组合学是一种组合学.
- 超立方体结构是一种超立方体结构.
背景情况:
- 立方图是超立方的子图.
- 图兰密度决定了图 H 是否在超立方子图中具有正比例的边缘.
- 层状图形是立方图形的一个特定子集.
研究的目的:
- 在超立方体内描述分层图形.
- 调查各种立方图的图兰密度,特别是分层和非分层的图.
- 扩大对图兰密度的理解,用于循环和超立方体中的细分.
主要方法:
- 专注于超立方体内的分层图形.
- 使用边缘颜色进行图形表征.
- 对图兰密度属性的细分和循环进行分析.
主要成果:
- 分层图形的特点是边缘颜色.
- 大多数非微不足道的分类在超立方体中表现出零图兰密度.
- 发现了具有正图兰密度和周长的非分层立方图形 8.
结论:
- 层状图在超立方体中具有不同的属性.
- 10周期的图兰密度仍然是一个悬而未决的问题,但它的极端数表现得独特.
- 这项研究促进了对超立方体结构中的图形属性和密度的理解.
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