English

Plane Triangulations Without Spanning 2-Trees

Combinatorics 2022-03-22 v1

Abstract

A 2-tree is a graph that can be formed by starting with a triangle and iterating the operation of making a new vertex adjacent to two adjacent vertices of the existing graph. Leizhen Cai asked in 1995 whether every maximal planar graph contains a spanning 2-tree. We answer this question in the negative by constructing an infinite class of maximal planar graphs that have no spanning 2-tree.

Keywords

Cite

@article{arxiv.2203.10239,
  title  = {Plane Triangulations Without Spanning 2-Trees},
  author = {Allan Bickle},
  journal= {arXiv preprint arXiv:2203.10239},
  year   = {2022}
}

Comments

9 pages

R2 v1 2026-06-24T10:18:59.450Z