The oriented relative clique number of triangle-free planar graphs is 10

Soura Sena Das; Soumen Nandi; Sagnik Sen

The oriented relative clique number of triangle-free planar graphs is 10

Discrete Mathematics 2022-08-23 v1 Combinatorics

Authors: Soura Sena Das , Soumen Nandi , Sagnik Sen

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.

Keywords

oriented relative clique number triangle-free planar graphs oriented coloring chromatic number oriented graph

Cite

@article{arxiv.2208.10188,
  title  = {The oriented relative clique number of triangle-free planar graphs is 10},
  author = {Soura Sena Das and Soumen Nandi and Sagnik Sen},
  journal= {arXiv preprint arXiv:2208.10188},
  year   = {2022}
}

The oriented relative clique number of triangle-free planar graphs is 10

Abstract

Keywords

Cite

Related papers