Local Boxicity, Local Dimension, and Maximum Degree
share
In this short note we focus on two recently introduced parameters in the literature, namely `local dimension' (a parameter on partially ordered sets) and `local boxicity' (a parameter on graphs). First we establish a relation between them and then we give an upper bound for both the parameters in terms of the maximum degree of a graph (for local dimension we consider the comparability graph of a poset). Finally, we show that the local boxicity of a graph is upper bounded by its `product dimension'.
READ FULL TEXT