Note on the number of edges in families with linear union-complexity

الأصل · EN

We give a simple argument showing that the number of edges in the intersection graph G of a family of n sets in the plane with a linear union-complexity is O(ω(G)n). In particular, we prove χ(G)≤ col(G)< 19ω(G) for intersection graph G of a family of pseudo-discs, which improves a previous bound.