The oriented relative clique number of triangle-free planar graphs is 10
share
In relation to oriented coloring and chromatic number, the parameter oriented relative clique number of an oriented graph G, denoted by ω_ro(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 ω_ro(G) is 10 when G is a planar graph.
READ FULL TEXT