Packing circuits in eulerian digraphs

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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Seymour, P.D. Packing circuits in eulerian digraphs. Combinatorica 16, 223–231 (1996). https://doi.org/10.1007/BF01844848

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Mathematics Subject Classification (1991)

  • 05 C 20
  • 05 C 70
  • 05 C 38