{Cn, C4}-Decomposition of the line graph of the complete graph

Abstract

For given positive integer n ≥ 4, let Cn, Kn and L(Kn) respectively denote a cycle with n edges, a complete graph on n vertices and the line graph of the complete graph Kn. For a given graph G, if H1, H2, ..., Hl are the edge disjoint subgraphs such that E(G) = E(H1) ∪ E(H2) ∪ ... ∪ E(Hl), then we say that H1, H2, ..., Hl decompose G. If G has a decomposition into copies of H1 and H2 using atleast one of each, then we say that G has a {H1, H2}-decomposition (or) G is {H1, H2}-decomposable. In this paper, it is proved that L(Kn) is {Cn, C4}-decomposable.