On friendliness between trees

Daria Kolodzey

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arXiv · 1509.00370

On friendliness between trees

Daria Kolodzey

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Abstract

The notion of friendliness between trees first appeared in solution of Lando's problem on intersection of polyhedra in 3-space. A tree is friendly to a path graph if edges of the tree can be numbered so that for each k,s the path between the edges k and k+1 contains either both or none of the edges k+2s,k+2s+1. Theorem. If a tree contains a path containing all vertices of degree greater than 2, then the tree is friendly to a path graph. We also prove another sufficient condition for friendliness to a path graph and a criterion for friendliness between trees, one of which has diameter 3.

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Daria Kolodzey. 2015-09-01. On friendliness between trees. https://arxiv.org/abs/1509.00370

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