# An Improved Lower Bound for Crossing Numbers

- Authors
- Publisher
- Springer Berlin / Heidelberg
- Publication Date
- Keywords

## Abstract

The crossing number of a graph G=(V,E), denoted by cr(G), is the smallest number of edge crossings in any drawing of G in the plane. Leighton [14] proved that for any n-vertex graph G of bounded degree, its crossing number satisfiescr(G) + n = Ω(bw2(G), wherebw(G) is the bisection width of G. The lower bound method was extended for graphs of arbitrary vertex degrees to cr in [15,19], where dv is the degree of any vertex v. We improve this bound by showing that the bisection width can be replaced by a larger parameter - the cutwidth of the graph. Our result also yields an upper bound for the path-width of G in term of its crossing number.

## There are no comments yet on this publication. Be the first to share your thoughts.