Scholarlink

<p>Transit functions were introduced as models of betweenness on undirected structures. Here we introduce directed transit function as the directed analogue on directed structures such as posets and directed graphs. We first show that betweenness in posets can be expressed by means of a simple set of first order axioms. Similar characterizations can be obtained for graphs with natural partial orders, in particular, forests, trees, and mangroves. Relaxing the acyclicity conditions leads to a generalization of the well-known geometric transit function to the directed structures. Moreover, we discuss some properties of the directed analogues of prominent transit functions, including the all-paths, induced paths, and shortest paths (or interval) transit functions. Finally we point out some open questions and directions for future work.</p>

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

Directed Transit Functions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月11日

查看全文
  • Arun Anil,
  • Manoj Changat,
  • John J. Chavara,
  • Lekshmi Kamal K-Sheela,
  • Prasanth G. Narasimha-Shenoi,
  • Bruno J. Schmidt,
  • Ameera Vaheeda Shanavas,
  • Peter F. Stadler

摘要

Transit functions were introduced as models of betweenness on undirected structures. Here we introduce directed transit function as the directed analogue on directed structures such as posets and directed graphs. We first show that betweenness in posets can be expressed by means of a simple set of first order axioms. Similar characterizations can be obtained for graphs with natural partial orders, in particular, forests, trees, and mangroves. Relaxing the acyclicity conditions leads to a generalization of the well-known geometric transit function to the directed structures. Moreover, we discuss some properties of the directed analogues of prominent transit functions, including the all-paths, induced paths, and shortest paths (or interval) transit functions. Finally we point out some open questions and directions for future work.