Scholarlink

We design a \(O(\log n)\) labeling scheme for planar graph embeddings. Given the labels of any two vertices we can directly determine whether the two vertices share a face. In the scheme, we use and design a \(O(\log n)\) labeling scheme for the property of two vertices sharing a common neighbor in a planar graph, a problem which we show to be equivalent to labeling for face-adjacency. We also prove a lower bound of \((1 + o(1))\log _2 n\) on label length.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Labeling Embeddings of Planar Graphs for Face-Adjacency

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Borna Šimić,
  • Roger Wattenhofer

摘要

We design a \(O(\log n)\) labeling scheme for planar graph embeddings. Given the labels of any two vertices we can directly determine whether the two vertices share a face. In the scheme, we use and design a \(O(\log n)\) labeling scheme for the property of two vertices sharing a common neighbor in a planar graph, a problem which we show to be equivalent to labeling for face-adjacency. We also prove a lower bound of \((1 + o(1))\log _2 n\) on label length.