Minimum (2,r)-metrics and integer multiflows
European Journal of Combinatorics - Special issue on discrete metric spaces
Minimum 0-extensions of graph metrics
European Journal of Combinatorics
Regular Article: Graphs of Some CAT(0) Complexes
Advances in Applied Mathematics
Tight spans of distances and the dual fractionality of undirected multiflow problems
Journal of Combinatorial Theory Series B
Half-integral five-terminus flows
Discrete Applied Mathematics
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We consider the multiflow feasibility problem whose demand graph is the vertex-disjoint union of two triangles. We show that this problem has a 1/12-integral solution whenever it is feasible and satisfies the Euler condition. This solves a conjecture raised by Karzanov, and completes the classification of the demand graphs having bounded fractionality. We reduce this problem to the multiflow maximization problem whose terminal weight is the graph metric of the complete bipartite graph, and show that it always has a 1/12-integral optimal multiflow for every inner Eulerian graph.