نتایج جستجو برای: edge decomposition

تعداد نتایج: 209257  

Journal: :Journal of Graph Theory 2006
János Barát Carsten Thomassen

We conjecture that, for each tree T , there exists a natural number kT such that the following holds: If G is a kT -edge-connected graph such that |E(T )| divides |E(G)|, then the edges of G can be divided into parts, each of which is isomorphic to T . We prove that for T = K1,3 (the claw), this holds if and only if there exists a (smallest) natural number kt such that every kt-edge-connected g...

2016
Saloua Senhaji Abdellah Aarab

Edge detection is one of the most commonly used operations in image analysis, and there are more algorithms in the literature for enhancing and detecting edges. Natural images contain both textured and untextured regions, so the cues of contour and texture are exploited simultaneously. In this paper, we present a new edge detection method for natural images using decomposition model. The main i...

Journal: :Australasian J. Combinatorics 2010
John Asplund Melissa S. Keranen

A decomposition of λ copies of monochromatic Kv into copies of K4 such that each copy of K4 contains at most one edge from each Kv is called a proper edge coloring of a BIBD(v, 4, λ). We show that the necessary conditions are sufficient for the existence of a BIBD(v, 4, λ) which has such a proper edge coloring.

Journal: :Graphs and Combinatorics 2003
Mariko Hagita André Kündgen Douglas B. West

In a graph G, the distance from an edge e to a set F ⊆ E(G) is the vertex distance from e to F in the line graph L(G). For a decomposition of E(G) into k sets, the distance vector of e is the k-tuple of distances from e to these sets. The decomposition dimension dec(G) of G is the smallest k such that G has a decomposition into k sets so that the distance vectors of the edges are distinct. For ...

Journal: :Discrete Applied Mathematics 2017
Ajit A. Diwan

A ~ P3-decomposition of a directed graph D is a partition of the arcs of D into directed paths of length 2. We characterize symmetric digraphs that do not admit a ~ P3-decomposition. We show that the only 2-regular, connected directed graphs that do not admit a ~ P3-decomposition are obtained from undirected odd cycles by replacing each edge by two oppositely directed arcs. In both cases, we gi...

2006
Stefan Szeider

Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.

Journal: :CoRR 2006
Marko Samer Stefan Szeider

Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.

2008
Zhengbing Bian Qian-Ping Gu

A graph of small branchwidth admits efficient dynamic programming algorithms for many NP-hard problems on the graph. A key step in these algorithms is to find a branch decomposition of small width for the graph. Given a planar graph G of n vertices, an optimal branch decomposition of G can be computed in polynomial time, e.g., by the edge-contraction method in O(n) time. All known algorithms fo...

2016
Fábio Botler Yoshiko Wakabayashi

A decomposition of a graph G is a set D = {H1, · · · , Hk} of pairwise edge-disjoint subgraphs of G that cover the set of edges of G. If Hi is isomorphic to a fixed graph H, for 1 ≤ i ≤ k, then we say that D is an H-decomposition of G. In this work, we study the case where H is a path of fixed length. For that, we first decompose the given graph into trails, and then we use a disentangling lemm...

Journal: :IEICE Transactions 2005
Kazuhiko Ushio Hideaki Fujimoto

Definition. Let Kn denote the complete graph of n vertices. The complete multigraph λKn is the complete graph Kn in which every edge is taken λ times. The t-foil (or the t-windmill) is a graph of t edge-disjoint K3’s with a common vertex and the common vertex is called the center of the t-foil. In particular, the 2-foil, the 3-foil, and the 4-foil are called the bowtie, the trefoil, and the qua...

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