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 , 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.
Document type :
Reports
Complete list of metadatas

Cited literature [9 references]  Display  Hide  Download

https://hal.inria.fr/hal-01247014
Contributor : Frederic Havet <>
Submitted on : Sunday, December 20, 2015 - 11:22:53 PM
Last modification on : Monday, November 5, 2018 - 3:36:03 PM
Long-term archiving on: Saturday, April 29, 2017 - 10:58:28 PM

File

RR-8833.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01247014, version 1

Citation

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⟩

Share

Metrics

Record views

788

Files downloads

543