On the mixed connectivity conjecture of Beineke and Harary

Sebastian S. Johann (), Sven O. Krumke () and Manuel Streicher ()
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Sebastian S. Johann: University of Kaiserslautern-Landau
Sven O. Krumke: University of Kaiserslautern-Landau
Manuel Streicher: University of Kaiserslautern-Landau

Annals of Operations Research, 2024, vol. 332, issue 1, No 6, 107-124

Abstract: Abstract The conjecture of Beineke and Harary states that for any two vertices which can be separated by k vertices and l edges for $$l\ge 1$$ l ≥ 1 but neither by k vertices and $$l-1$$ l - 1 edges nor $$k-1$$ k - 1 vertices and l edges there are $$k+l$$ k + l edge-disjoint paths connecting these two vertices of which $$k+1$$ k + 1 are internally disjoint.In this paper we prove this conjecture for $$l=2$$ l = 2 and every $$k\in \mathbb {N}$$ k ∈ N .We utilize this result to prove that the conjecture holds for all graphs of treewidth at most 3 and all k and l.

Keywords: Mixed connectivity; Mixed cut; Menger; Graph theory; 05C40; 05C38 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05527-8

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