Lattice Path Matroids are 3-Colorable
arXiv:1807.00585
Abstract
We show that every lattice path matroid of rank at least two has a quite simple coline, also known as a positive coline. Therefore every orientation of a lattice path matroid is 3-colorable with respect to the chromatic number of oriented matroids introduced by J. Nešetřil, R. Nickel, and W. Hochstättler.