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}
}
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9 pages