On the 4-girth-thickness of the line graph of the complete graph

Abstract

The p-girth-thickness 0(g, G) of a graph G is the minimum number of planar subgraphs of girth at least g whose union is G. In this note, we give the 4-girth-thickness 0(4, L(Kn)) of the line graph of the complete graph L(Kn) when n is even. We also give the minimum number of subgraphs of L(Kn), which are of girth at least 4 and embeddable on the projective plane, whose union is L(Kn). © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.