The strong vertex span of trees

Fuente: arXiv
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Main Authors: Grašič, Mateja, Mouron, Chris, Taranenko, Andrej
Format: Preprint
Published: 2024
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author Grašič, Mateja
Mouron, Chris
Taranenko, Andrej
author_facet Grašič, Mateja
Mouron, Chris
Taranenko, Andrej
contents The strong vertex (edge) span of a given graph $G$ is the maximum distance that two players can maintain at all times while visiting all vertices (edges) of $G$ and moving either to an adjacent vertex or staying in the current position independently of each other. We introduce the notions of switching walks and triod size of a tree, which are used to determine the strong vertex and the strong edge span of an arbitrary tree. The obtained results are used in an algorithm that computes the strong vertex (edge) span of the input tree in linear time.
format Preprint
id arxiv_https___arxiv_org_abs_2412_03266
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The strong vertex span of trees
Grašič, Mateja
Mouron, Chris
Taranenko, Andrej
Combinatorics
Discrete Mathematics
05C05, 05C85
The strong vertex (edge) span of a given graph $G$ is the maximum distance that two players can maintain at all times while visiting all vertices (edges) of $G$ and moving either to an adjacent vertex or staying in the current position independently of each other. We introduce the notions of switching walks and triod size of a tree, which are used to determine the strong vertex and the strong edge span of an arbitrary tree. The obtained results are used in an algorithm that computes the strong vertex (edge) span of the input tree in linear time.
title The strong vertex span of trees
topic Combinatorics
Discrete Mathematics
05C05, 05C85
url https://arxiv.org/abs/2412.03266