Cyclic orders: Equivalence and duality

@article{Charbit2008CyclicOE,
  title={Cyclic orders: Equivalence and duality},
  author={Pierre Charbit and Andr{\'a}s Seb{\"o}},
  journal={Combinatorica},
  year={2008},
  volume={28},
  pages={131-143}
}
Cyclic orders of graphs and their equivalence have been promoted by Bessy and Thomassés recent proof of Gallai’s conjecture. We explore this notion further : we prove that two cyclic orders are equivalent if and only if the index of every circuit is the same in the two. The proof is short and provides a good characterization and a polynomial algorithm for deciding whether two orders are equivalent. We then derive short proofs of Gallai’s conjecture and a “polar” result of Bessy and Thomassé’s… CONTINUE READING

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Problem 15

  • T. Gallai
  • Theory of Graphs and its Applications (M. Fiedler…
  • 1964

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