A matchingM is uniquely restricted in a graph G if its saturated vertices induce a subgraph which has a unique perfect matching, namely M itself [M.C. Golumbic, T. Hirst, M. Lewenstein, Uniquely restricted matchings, Algorithmica 31 (2001) 139–154]. G is a König–Egerváry graph provided (G)+ (G)= |V (G)| [R.W. Deming, Independence numbers of graphs—an extension of the König–Egerváry theorem, Dis...

If n = 2, then the set j£ is closely related to the Fibonacci sequence; specifically, t GT2 iff the 7 term of the Fibonacci sequence is odd. We ask, for each w, which numbers are uniquely expressible as the sum of two distinct elements of Tn. In general, for any given w, one can determine exactly which numbers are uniquely expressible. If w = 2, it is easy to see that there are five such number...

This paper discusses the manipulation of multiple objects grasped by the enveloping grasp. In case of the enveloping grasp, since the contact force cannot be uniquely determined for a given joint torque, the resultant force also cannot be obtained uniquely. We derive a joint torque set enabling the resultant force set directing the desired direction. First, we extract the feature of the contact...

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...

A maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph spanned by S∪N(S), where N(S) is the neighborhood of S. A matching M is uniquely restricted if its saturated vertices induce a subgraph which has a unique perfect matching, namely M itself. Nemhauser and Trotter Jr. [12], pr...

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...