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Almost disjoint spanning trees: relaxing the conditions for completely independent spanning trees

Abstract : The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by defining (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges, respectively) that are shared by more than one tree. We illustrate how (i, j)-disjoint spanning trees provide some nuances between the existence of disjoint connected dominating sets and completely independent spanning trees. We prove that determining if there exist two (i, j)-disjoint spanning trees in a graph G is NP-complete, for every two positive integers i and j. Moreover we prove that for square of graphs, k-connected interval graphs, complete graphs and several grids, there exist (i, j)-disjoint spanning trees for interesting values of i and j.
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https://hal.archives-ouvertes.fr/hal-01476364
Contributor : Nicolas Gastineau <>
Submitted on : Friday, February 24, 2017 - 6:06:35 PM
Last modification on : Monday, March 30, 2020 - 8:45:19 AM
Document(s) archivé(s) le : Thursday, May 25, 2017 - 2:20:16 PM

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  • HAL Id : hal-01476364, version 1
  • ARXIV : 1702.08289

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Benoit Darties, Nicolas Gastineau, Olivier Togni. Almost disjoint spanning trees: relaxing the conditions for completely independent spanning trees. 2017. ⟨hal-01476364⟩

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