We prove that, if a graph G (without multiple edges) has maximum degree d and edge-chromatic number d + 1, then G contains two distinct vertices x, y and a collection of d pairwise edge-disjoint paths between x and y. In particular, the line graph of G satisfies Hajós’ conjecture. © 2006 Elsevier Inc. All rights reserved.

In this paper, the analytical solution of an electric and Volterra edge dislocation in a functionally graded piezoelectric (FGP) medium is obtained by means of complex Fourier transform. The system is subjected to in-plane mechanical and electrical loading. The material properties of the medium vary exponentially with coordinating parallel to the crack. In this study, the rate of the gradual ch...

We present a novel semi-local image descriptor which encodes multiple edges corresponding to the image structure boundaries around an interest point. The proposed method addresses the problem of poor edge detection through a robust, scale and orientation invariant, descriptor distance. In addition, a clustering of descriptors capable of extracting distinctive shapes from a set of descriptors is...

Let G = (V; E) be a /nite and undirected graph without loops and multiple edges. An edge is said to dominate itself and any edge adjacent to it. A subset D of E is called a perfect edge dominating set if every edge of E \ D is dominated by exactly one edge in D and an e cient edge dominating set if every edge of E is dominated by exactly one edge in D. The perfect (e cient) edge domination prob...