The dimension of a poset $ P $ is the minimum number of total orders whose intersection is
$ P $. We prove that the dimension of every poset whose comparability graph has maximum …

The boxicity of a graph G=(V, E), denoted by box (G), is the minimum dimension d such that
G is the intersection graph of a family (B v) v∈ V of d-dimensional axis-parallel boxes in R d …

The cop number of a graph G is the smallest k such that k cops win the game of cops and
robber on G. We investigate the maximum cop number of geometric intersection graphs …

Geometric intersection graphs are graphs arising from families of geometric objects in the
plane (and, more generally, in R^ d). This class has captured the attention of many …

The boxicity of a graph is the smallest dimension d allowing a representation of it as the
intersection graph of a set of d-dimensional axis-parallel boxes. We present a simple …

Let $ box (G) $ be the boxicity of a graph $ G $, $ G [H_1, H_2,\ldots, H_n] $ be the $ G $-
generalized join graph of $ n $-pairwise disjoint graphs $ H_1, H_2,\ldots, H_n $, $ G^ d_k …

The boxicity of a graph G=(V, E) is the smallest integer k for which there exist k interval
graphs G i=(V, E i), 1⩽ i⩽ k, such that E= E 1∩⋯∩ E k. In the first part of this note, we prove …

In this short note, we relate the boxicity of graphs (and the dimension of posets) with their
generalized coloring parameters. In particular, together with known estimates, our results …

A family F of permutations of the vertices of a hypergraph H is called pairwise suitable for H
if, for every pair of disjoint edges in H, there exists a permutation in F in which all the vertices …

The boxicity of a graph is the smallest dimension $ d $ allowing a representation of it as the
intersection graph of a set of $ d $-dimensional axis-parallel boxes. We present a simple …