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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics