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Article Dans Une Revue Graphs and Combinatorics Année : 2022

Non-separating Spanning Trees and Out-Branchings in Digraphs of Independence Number 2

Jørgen Bang-Jensen
Stéphane Bessy
Anders Yeo
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Résumé

A subgraph H= (V, F) of a graph G= (V,E) is non-separating if G-F, that is, the graph obtained from G by deleting the edges in F, is connected. Analogously we say that a subdigraph X= (V,B) of a digraph D= (V,A) is non-separating if D-B is strongly connected. We study non-separating spanning trees and out-branchings in digraphs of independence number 2. Our main results are that every 2-arc-strong digraph D of independence number alpha(D) = 2 and minimum in-degree at least 5 and every 2-arc-strong oriented graph with alpha(D) = 2 and minimum in-degree at least 3 has a non-separating out-branching and minimum in-degree 2 is not enough. We also prove a number of other results, including that every 2-arc-strong digraph D with alpha(D)<=2 and at least 14 vertices has a non-separating spanning tree and that every graph G with delta(G)>=4 and alpha(G) = 2 has a non-separating hamiltonian path.
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Dates et versions

hal-04032270 , version 1 (17-10-2023)

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Jørgen Bang-Jensen, Stéphane Bessy, Anders Yeo. Non-separating Spanning Trees and Out-Branchings in Digraphs of Independence Number 2. Graphs and Combinatorics, 2022, 38 (6), ⟨10.1007/s00373-022-02589-6⟩. ⟨hal-04032270⟩
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