The edge-disjoint paths problem in Eulerian graphs and 4-edge-connected graphs
If an input graph is either 4-edge-connected or Eulerian, then our algorithm only needs to look for the following three simple reductions: (i) Excluding vertices of high degree. (ii) Excluding ≤3-edge-cuts. (iii) Excluding large clique minors.
When an input graph is either 4-edge-connected or Eulerian, the number of terminals k is allowed to be a non-trivially super constant number, up to k=O((log log logn)½−ε) for any ε > 0. In addition, if an input graph is either 4-edge-connected planar or Eulerian planar, k is allowed to be O((logn½−ε) for any ε > 0.
We also give our own algorithm for the edge-disjoint paths problem in general graphs. We basically follow the Robertson-Seymour’s algorithm, but we cut half of the proof of the correctness for their algorithm. In addition, our algorithm is faster than Robertson and Seymour’s.
Mathematics Subject Classification (2000)05C38 05C83 05C85
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