LINE GRAPHS CONTAINING {1, 2}-FACTORS

Let G be a graph. A spanning subgraph H of G is called a {1, 2}-factor if each component of H is either a copy of K 2 or a 2-regular subgraph of G. In this article we characterize all graphs whose permanent of their adjacency matrices are 1. Then we prove that the line graph of G, L(G), admits a {1, 2}-factor, unless G is isomorphic to a spanning tree of a graph whose permanent of the adjacency matrix is 1 and in addition contains a unique perfect matching.