On terminal delta-wye reducibility of planar graphs

@article{Gitler2011OnTD,
  title={On terminal delta-wye reducibility of planar graphs},
  author={I. Gitler and F. Sagols},
  journal={Networks},
  year={2011},
  volume={57},
  pages={174-186}
}
We prove terminal Δ-Y reducibility of planar graphs with at most three terminals. The most important consequence of our proof is that this implicitly gives an efficient algorithm with time complexity O(|E(G)|4) for reducibility of planar graphs G with at most three terminals. It also can be used for restricted reducibility problems with more terminals. Our proof uses a very well-known translation from these operations to transformations on the medial graph. © 2010 Wiley Periodicals, Inc… Expand
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References

SHOWING 1-10 OF 23 REFERENCES
On the delta-wye reduction for planar graphs
  • K. Truemper
  • Mathematics, Computer Science
  • J. Graph Theory
  • 1989
  • 51
Delta-Wye Transformations and the Efficient Reduction of Two-Terminal Planar Graphs
  • 44
On the uniqueness of kernels
  • A. Schrijver
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1992
  • 13
Convex Polytopes
  • 1,227
  • Highly Influential
  • PDF
Algorithmic issues on planar terminal ∆ ↔ Y reducibility
  • preprint
  • 2004
Algorithmic issues on planar terminal ∆ ↔ Y reducibility, preprint
  • Algorithmic issues on planar terminal ∆ ↔ Y reducibility, preprint
  • 2004
Four terminal reducibility and projective planar ∆ ↔ Y reducible graphs
  • J. Graph Theory
  • 2000
...
1
2
3
...