A mixed version of Menger's theorem


An(a, b)-n-fan means a union ofn internally disjoint paths. Menger's theorem states that a graphG has an(a, b)-n-fan if and only ifG isn-connected betweena andb. We show thatG contains λ edge-disjoint(a, b)-n-fans if and only if for anyk withk≤0≤min{n−1, |V(G)|−2} and for any subsetX ofV(G)-{a, b} with cardinalityk, G-X is λ(n-k)-edge-connected betweena andb.

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Egawa, Y., Kaneko, A. & Matsumoto, M. A mixed version of Menger's theorem. Combinatorica 11, 71–74 (1991). https://doi.org/10.1007/BF01375475

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  • 05 C 40