论文信息 - A mixed version of Menger's theorem

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.

[1] K. Menger. Zur allgemeinen Kurventheorie , 1927 .

[2] D. R. Fulkerson,et al. Flows in Networks. , 1964 .

[3] G. Dirac. In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen† , 1960 .

[4] G. Chartrand,et al. Graphs & Digraphs , 1986 .

[5] B. Bollobás,et al. Extremal Graph Theory , 2013 .

[6] D. König. Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre , 1916 .