A k-chromatic graph G is called uniquely k-colorable if every k-coloring of the vertex set V of G induces the same partition of V into k color classes. There is an innnite class C of uniquely 4-colorable planar graphs obtained from the K 4 by repeatedly inserting new vertices of degree 3 in triangular faces. In this paper we are concerned with the well-known conjecture (see 6]) that every uniqu...

The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted matching in a bipartite graph is equivalent to recognition a acyclic digraph. Based on these results, it proves that determine the bipartite graphs with all maxim...

We study the Unique Set Cover problem on unit disks and unit squares. For a given set P of n points and a set D of m geometric objects both in the plane, the objective of the Unique Set Cover problem is to select a subset D′ ⊆ D of objects such that every point in P is covered by at least one object in D′ and the number of points covered uniquely is maximized, where a point is covered uniquely ...

Given a graph F , a graph G is uniquely F -saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F . In this paper we study uniquely Ct-saturated graphs. We prove the following: (1) a graph is uniquely C5-saturated if and only if it is a friendship graph. (2) There are no uniquely C6-saturated graphs or uniquely C7-saturated graphs. (3) F...

A graph G is uniquely Kr-saturated if it contains no clique with r vertices and if for all edges e in the complement, G + e has a unique clique with r vertices. Previously, few examples of uniquely Kr-saturated graphs were known, and little was known about their properties. We search for these graphs by adapting orbital branching, a technique originally developed for symmetric integer linear pr...

Fault detection and isolation in dynamic physical systems based on analysis of transient system behavior involves monitoring for deviations and linking observed deviations to changes in system parameters. Components linked to the changed parameter values may be faulty. Functional redundancy is exploited in choosing measurements to uniquely isolate all faults. Measurement selection algorithms de...

This paper presents a full generalization of Bohr’s equivalence theorem for the case almost periodic functions, which improves recent result that was uniquely formulated in existence an integral basis set exponents associated Dirichlet series.