### Abstract

Let c(x,y) denote the maximum number of edge-disjoint directed paths joining x to y in the digraph G. It is shown that, for a given point a of G, c(a,x) ≤ c(x,a) for any x implies that the outdegree of a is ≤ its indegree. An immediate consequence is Kotzig's conjecture: Given a digraph G, c(x,y) = c(y,x) for every x, y if and only if the graph is pseudo-symmetric, i.e., each point has the same indegree and outdegree (the "if" part having been proved by Kotzig). The same method is applied to prove a weakened form of a conjecture of N. Robertson, while the original conjecture is disproved.

Original language | English |
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Pages (from-to) | 174-177 |

Number of pages | 4 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 15 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 1973 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics