The oriented relative clique number of triangle-free planar graphs is 10
Abstract
In relation to oriented coloring and chromatic number, the parameter oriented relative clique number of an oriented graph G, denoted by ωro(G), is the main focus of this work. We solve an open problem mentioned in the recent survey on oriented coloring by Sopena (Discrete Mathematics 2016), and positively settle a conjecture due to Sen (PhD thesis 2014), by proving that the maximum value of ωro(G) is 10 when G is a planar graph.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.