Emergent Mind
The oriented relative clique number of triangle-free planar graphs is 10
(2208.10188)
Published Aug 22, 2022
in
cs.DM
and
math.CO
Abstract
In relation to oriented coloring and chromatic number, the parameter oriented relative clique number of an oriented graph $\overrightarrow{G}$, denoted by $\omega{ro}(\overrightarrow{G})$, 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 $\omega{ro}(\overrightarrow{G})$ is $10$ when $\overrightarrow{G}$ is a planar graph.
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