A decomposition of a graph is a partition of the edge set, giving a set of subgraphs. A transitive decomposition is a decomposition which is highly symmetrical, in the sense that the subgraphs are preserved and transitively permuted by a group of automorphisms of the graph. This paper describes some ‘product’ constructions for transitive decompositions of graphs, and shows how these may be used...

We give a complete solution to the existence problem for complementary P3-decompositions of the complete multigraph, where P 3 denotes the path of length 3. A complementary decomposition 2>.K v (P 3 , P 3) is an edge decomposition of the complete multigraph >'Kv into P 3 '8 with the property that upon taking the complement of each path one obtains a second decomposition of >'K3 into P3 '8 (wher...

Let G be an undirected bipartite graph with positive integer weights on the edges. We refine the existing decomposition theorem originally proposed by Kao et al., for computing maximum weight bipartite matching. We apply it to design an efficient version of the decomposition algorithm to compute the weight of a maximum weight bipartite matching of G in O( √ |V |W ′/k(|V |,W ′/N))-time by employ...

In this paper we give a linear algorithm to edge partition a toroidal graph, i.e., graph that can be embedded on the orientable surface of genus one without edge crossing, into three forests plus a set of at most three edges. For triangulated toroidal graphs, this algorithm gives a linear algorithm for finding three edge-disjoint spanning trees. This is in a certain way an extension of the well...

In this paper, we present a new graph model of sparse matrix decomposition for parallel sparse matrix–vector multiplication. Our model differs from previous graph-based approaches in two main respects. Firstly, our model is based on edge colouring rather than vertex partitioning. Secondly, our model is able to correctly quantify and minimise the total communication volume of the parallel sparse...

1 Edge-disjoint decompositions Some of the graphs in this section are allowed to have multiple edges. They will be referred to as multigraphs. All graphs are assumed to have vertex set [n] = {1, 2, . . . , n}. Multiple edges between vertices of a multigraph G are regarded as distinct members of its edge set, E(G). We say that a collection of multigraphs1 Gi, i ∈ [m] is an edge-disjoint decompos...

Our main result essentially reduces the problem of finding an edge-decomposition of a balanced r-partite graph of large minimum degree into r-cliques to the problem of finding a fractional r-clique decomposition or an approximate one. Together with very recent results of Bowditch and Dukes as well as Montgomery on fractional decompositions into triangles and cliques respectively, this gives the...

A T -decomposition of a graph G is a set of edge-disjoint copies of T in G that cover the edge set of G. Graham and Häggkvist (1989) conjectured that any 2l-regular graph G admits a T -decomposition if T is a tree with l edges. Kouider and Lonc (1999) conjectured that, in the special case where T is the path with l edges, G admits a T -decomposition D where every vertex of G is the end-vertex o...

—This paper proposes an edge detection algorithm based on adaptive threshold which is obtained by histogram matching edge gradient value. The implementation of this algorithm is made up of three procedures: all phase discrete cosine sequency filtering, wavelet decomposition and adaptive threshold processing. The image is decomposed into low frequency and high frequency subbands by using all ph...

It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C3, C4, C5, and K4 − e have no such decompositions. We construct an infinite sequence {Fi}∞i=0 of nondecomposable graphs. On the other hand, we prove that every...