# Hoàng-Reed conjecture holds for tournaments

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : Hoàng-Reed conjecture asserts that every digraph $D$ has a collection $\cal C$ of circuits $C_1,\dots,C_{\delta ^+}$, where $\delta ^+$ is the minimum outdegree of $D$, such that the circuits of $\cal C$ have a forest-like structure. Formally, $|V(C_i)\cap (V(C_1)\cup \dots \cup V(C_{i-1}))|\leq 1$, for all $i=2,\dots ,\delta^+$. We verify this conjecture for the class of tournaments.
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https://hal.inria.fr/inria-00091366
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Submitted on : Friday, September 15, 2006 - 11:22:26 AM
Last modification on : Monday, October 12, 2020 - 10:30:26 AM
Long-term archiving on: : Monday, September 20, 2010 - 4:22:13 PM

### Identifiers

• HAL Id : inria-00091366, version 2

### Citation

Frédéric Havet, Stéphan Thomassé, Anders Yeo. Hoàng-Reed conjecture holds for tournaments. [Research Report] RR-5976, INRIA. 2006, pp.7. ⟨inria-00091366v2⟩

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