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Proper orientation of cacti

Julio Araujo 1 Frédéric Havet 2 Claudia Linhares Sales 1 Ana Silva 1
1 ParGO - Parallelism, Graphs and Optimization Research Group
2 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : An orientation of a graph is proper if two adjacent vertices have different indegrees. We prove that every cactus admits a proper orientation with maximum indegree at most 7. We also prove that the bound 7 is tight by showing a cactus having no proper orientation with maximum indegree less than 7. We also prove that any planar claw-free graph has a proper orientation with maximum indegree at most 6 and that this bound can also be attained.
Keywords : proper orientation graph coloring cactus graph claw-free graph
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https://hal.inria.fr/hal-01247014
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Submitted on : Sunday, December 20, 2015 - 11:22:53 PM
Last modification on : Thursday, January 20, 2022 - 5:32:34 PM
Long-term archiving on: : Saturday, April 29, 2017 - 10:58:28 PM

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  • HAL Id : hal-01247014, version 1

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CNRS | INRIA | I3S | INRIA-RRRT | LARA | TDS-MACS | UNIV-COTEDAZUR

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Julio Araujo, Frédéric Havet, Claudia Linhares Sales, Ana Silva. Proper orientation of cacti. [Research Report] RR-8833, INRIA Sophia Antipolis - Méditerranée. 2015, pp.17. ⟨hal-01247014⟩

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