cross-index | crossing parameter

The local crossing number is defined as the least nonnegative integer k such that the graph has a k-planar drawing. In other words, it is the smallest possible number of times that a single edge in a graph is crossed over all possible graph drawings. Guy et al. (1968) attribute the definition to unpublished work of Ringel. The local crossing number of a graph is called the cross-index by Thomassen and sometimes also the crossing parameter, but Schaefer strongly encourages the use of "local crossing number." The term "planarity" might be both more descriptive and more concise. Schaefer and Ábrego and Fernández-Merchant denote the local crossing number of a graph G as lcr(G).

graph crossing number | k-planar graph | rectilinear local crossing number