Packings of graphs and applications to computational complexity


Let G1 and G2 be graphs with n vertices. If there are edge-disjoint copies of G1 and G1 with the same n vertices, then we say there is a packing of G1 and G2. This paper is concerned with establishing conditions on G1 and G2 under which there is a packing. Our main result (Theorem 1) shows that, with very few exceptions, if G1 and G2 together have at most 2n-3 edges and no vertex is joined to all other vertices, then there is a packing of G1 and G2. Our packing results have some applications to computational complexity. In particular, we show that, for subgraphs of tournaments, the property of containing a sink is a monotone property with minimal computational complexity. © 1978.

Publication Title

Journal of Combinatorial Theory, Series B