Abstract
LetG be an eulerian digraph; let ν(G) be the maximum number of pairwise edge-disjoint directed circuits ofG, and τ(G) the smallest size of a set of edges that meets all directed circuits ofG. Borobia, Nutov and Penn showed that ν(G) need not be equal to τ(G). We show that ν(G)=τ(G) provided thatG has a “linkless” embedding in 3-space, or equivalently, if no minor ofG can be converted toK 6 by Δ−Y andY−Δ operations.
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References
A. Borobia, Z. Nutov, andM. Penn: On doubly stochastic and non-identity permutation matrices, manuscript 1994.
L. Lovász: On two minimax theorems in graph theory.J. Combin. Theory, Ser. B,21 (1976), 96–103.
C. L. Lucchesi, andD. H. Younger: A minimax relation for directed graphs,J. London Math. Soc.,17 (1978), 369–374.
N. Robertson, P. D. Seymour, andR. Thomas: Sachs' linkless embedding conjecture,J. Combin. Theory, Ser. B,64 (1995), 185–227.