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Reports (Research Report) Year : 2015

Proper orientation of cacti

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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.
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Dates and versions

hal-01247014 , version 1 (20-12-2015)

Identifiers

  • HAL Id : hal-01247014 , version 1

Cite

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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