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Cyclic Orders: Equivalence and Duality

Abstract : Cyclic orders of graphs and their equivalence have been promoted by Bessy and Thomass\'{e}s recent proof of Gallai's conjecture. We explore this notion further : we prove that two cyclic orders are equivalent if and only if the winding number 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 Thomass\'{e}'s using the duality theorem of linear programming, total unimodularity, and the new result on the equivalence of cyclic orders.
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https://hal.archives-ouvertes.fr/hal-00005192
Contributor : Jacky Coutin <>
Submitted on : Wednesday, June 7, 2006 - 2:50:25 PM
Last modification on : Tuesday, July 6, 2021 - 2:56:02 PM
Long-term archiving on: : Thursday, April 1, 2010 - 9:38:02 PM

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  • HAL Id : hal-00005192, version 1

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András Sebő, Pierre Charbit. Cyclic Orders: Equivalence and Duality. 2006. ⟨hal-00005192⟩

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