Boxicity of line graphs
The boxicity of a graph H, denoted by box ( H), is the minimum integer k such that H is an intersection graph of axis-parallel k -dimensional boxes in R k. In this paper we show that for a line graph G of a multigraph, box ( G) ≤ 2 Δ ( G) ( ⌈ log 2 log 2 Δ ( G) ⌉ + 3) + 1, where Δ ( G) denotes the maximum degree of G.