Geodesic
Hindrance from a wasteful partial linkage
The electronic journal of combinatorics, Tome 32 (2025) no. 3
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Let $D=(V,E)$ be a (possibly infinite) digraph and $A,B\subseteq V$. A hindrance consists of an $AB$-separator $S$ together with a set of disjoint $AS$-paths linking a proper subset of $A$ onto $S$. Hindrances and configurations guaranteeing the existence of hindrances play an essential role in the proof of the infinite version of Menger's theorem and are important in the context of certain open problems as well. This motivates the investigation of circumstances under which hindrances appear. In this paper we show that if there is a "wasteful partial linkage", i.e. a set $\mathcal{P}$ of disjoint $AB$-paths with fewer unused vertices in $B$ than in $A$, then there exists a hindrance.
DOI : 10.37236/13730
Classification : 05C20, 05C63, 05C40
Mots-clés : hindered web, partially linked web 
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     author = {Attila Jo\'o},
     title = {Hindrance from a wasteful partial linkage},
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     year = {2025},
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     number = {3},
     doi = {10.37236/13730},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/13730/}
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Attila Joó. Hindrance from a wasteful partial linkage. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13730

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