We present a strengthening of the countable Menger theorem [Aharoni, 1987] (edge version) of R. Aharoni (see also in [Diestel, 2005, p. 217]) by placing a finitary matroid on the ingoing edges of each vertex and demanding the path-system to use an independent set of ingoing edges at any vertex. Our result is the complementarity condition based generalization of the minimax theorem that one can prove in the finite case about the maximal possible size of the path-system.
Bibtex entry:
@techreport{egres-16-17,
AUTHOR | = | {Jo{\'o}, Attila}, |
TITLE | = | {Countable Menger theorem with finitary matroid constraints on the ingoing edges}, |
NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2016}, |
NUMBER | = | {TR-2016-17} |