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math.CO2026
An approximate cactus-decomposition for vertex-connectivity
Romain Bourneuf, Johannes Carmesin, Jan Kurkofka +1
The classical cactus theorem of Dinitz, Karzanov and Lomonosov from 1976 states that the minimum edge-cuts of a connected graph are displayed by a cactus. For vertex-separations, T…
math.CO2026
A characterisation of all vertex-transitive finite graphs of connectivity < 5
Jan Kurkofka, Tim Planken
We characterise all vertex-transitive finite connected graphs as essentially 5-connected or on a short list of explicit graph-classes. Our proof heavily uses Tutte-type canonical d…