Proper orientation of cacti

Julio Araujo 1 Frédéric Havet 2 Claudia Linhares Sales 1 Ana Silva 1
2 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , 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.
Type de document :
Rapport
[Research Report] RR-8833, INRIA Sophia Antipolis - Méditerranée. 2015, pp.17


https://hal.inria.fr/hal-01247014
Contributeur : Frederic Havet <>
Soumis le : dimanche 20 décembre 2015 - 23:22:53
Dernière modification le : vendredi 16 septembre 2016 - 15:13:51

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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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