We consider two generalizations of the edge coloring problem in bipartite graphs. The first problem we consider is the weighted bipartite edge coloring problem where we are given an edge-weighted bipartite graph G = (V, E) with weights w : E → [0, 1]. The task is to find a proper weighted coloring of the edges with as few colors as possible. An edge coloring of the weighted graph is called a pr...

In this paper, an improved DWT based edge detection algorithm for noisy images has been proposed. The proposed edge detection method works efficiently on images influenced by noise and is able to differentiate between noise and real edges, thus detecting the actual edges. In the proposed algorithm the DWT edge detector separates detail coefficients at the time of decomposition, thus it has to e...

Crack evaluation is essential for effective classification of pavement cracks. Digital images of pavement cracks have been analyzed using techniques such as fuzzy set theory and neural networks. Bidimensional empirical mode decomposition (BEMD), a new image analysis method recently developed, can potentially be used for pavement crack evaluation. BEMD is an extension of the empirical mode decom...

The network reliability analysis based on Binary Decision Diagram (BDD) consists of three steps: edge ordering, BDD generation and BDD evaluation. The BDD generation process using edge expansion technique should recursively decompose the network and construct the edge expansion subnet in a top-down manner. There is large number of useless or redundant subnets generated in this decomposition, wh...

Abstract The problem of efficiently computing all $$k$$ k -edge-connected components ( -ECCs) a graph G for user-given k has been extensively studied recently in view its importance many applications. -ECCs possible values form hierarchical structure; that is, any two different the same value are disjoint and...

This thesis focuses on two topics of graph algorithms. The first topic is network inference. How efficiently can we find an unknown graph using shortest path queries between its vertices? We assume that the graph has bounded degree. In the reconstruction problem, the goal is to find the graph; and in the verification problem, the goal is to check whether a given graph is correct. We provide ran...

We study edge-decompositions of highly connected graphs into copies of a given tree. In particular we attack the following conjecture by Barát and Thomassen: for each tree T , there exists a natural number kT such that if G is a kT -edge-connected graph, and |E(T )| divides |E(G)|, then E(G) has a decomposition into copies of T . As one of our main results it is sufficient to prove the conjectu...

Let n ≥ 5 be an odd integer and K n the complete graph on n vertices. Let i be an integer with 2 ≤ i ≤ (n − 1)/2. A hamiltonian decomposition H of K n is called i-perfect if the set of the chords at distance i of the hamiltonian cycles in H is the edge set of K n. We show that there exists a 3-perfect hamiltonian decomposition of K n for all odd n ≥ 7.

Barát and Thomassen (2006) posed the following decomposition conjecture: for each tree T , there exists a natural number kT such that, if G is a kT -edge-connected graph and |E(G)| is divisible by |E(T )|, then G admits a decomposition into copies of T . In a series of papers, Thomassen verified this conjecture for stars, some bistars, paths of length 3, and paths whose length is a power of 2. ...