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.
https://hal.inria.fr/hal-01247014
Contributor : Frederic Havet
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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
