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 <>
Submitted on : Sunday, December 20, 2015 - 11:22:53 PM Last modification on : Monday, October 12, 2020 - 10:30:39 AM Long-term archiving on: : Saturday, April 29, 2017 - 10:58:28 PM