Eccentric coloring is a new variation of coloring, where higher numbered colors can not be used as freely as lower numbered colors. In addition there is a correspondence between the eccentricity (max distance) of a vertex and the highest legal color for that vertex. In this note we investigate eccentric coloring of trees. We give the eccentric chromatic number or a bound on the eccentric chroma...

Due to the rapid development of information technologies, especially the network technologies, business activities have never been as integrated as they are now. Business decision making often requires gathering information from different sources. This dissertation focuses on the problem of entity matching, associating corresponding information elements within or across information systems. It ...

In this paper, we propose a modified approach for the basic meet-in-the-middle attack which we call differential sieving for 2-step matching. This technique improves the scope of the basic meet in the middle attack by providing means to extend the matching point for an extra round through differential matching and hence the overall number of the attacked rounds is extended. Our approach starts ...

Abstract The well-known -complete problem Matching Cut is to decide if a graph has matching that also an edge cut of the graph. We prove new complexity results for restricted H -free graphs, is, graphs do not contain some fixed as induced subgraph. two recently studied variants , on graphs. first variant requires must be extendable perfect second matching. In particular, we there exists small c...

A set $Wsubset V (G)$ is called a resolving set, if for every two distinct vertices $u, v in V (G)$ there exists $win W$ such that $d(u,w) not = d(v,w)$, where $d(x, y)$ is the distance between the vertices $x$ and $y$. A resolving set for $G$ with minimum cardinality is called a metric basis. A graph with a unique metric basis is called a uniquely dimensional graph. In this paper, we establish...

A mixed hypergraph consists of two families of edges: the C-edges and D-edges. In a coloring every C-edge has at least two vertices of the same color, while every D-edge has at least two vertices colored differently. The largest and smallest possible numbers of colors in a coloring are termed the upper and lower chromatic number, χ̄ and χ, respectively. A mixed hypergraph is called uniquely colo...

We characterize the set of extreme points monotonic functions that are either majorized by a given function f or themselves majorize and show these play crucial role in many economic design problems. Our main results each point is uniquely characterized countable collection intervals. Outside intervals equals original inside constant. Further consistency conditions need to be satisfied pinning ...