For a set D of positive integers, we define a vertex set S ⊆ V (G) to be D-independent if u, v ∈ S implies the distance d(u, v) 6∈ D. The D-independence number βD(G) is the maximum cardinality of a D-independent set. In particular, the independence number β(G) = β{1}(G). Along with general results we consider, in particular, the odd-independence number βODD(G) where ODD = {1, 3, 5, . . .}.

Let G = (V,E). A set S ⊆ V is independent if no two vertices from S are adjacent, and by Ind(G) we mean the set of all independent sets of G. The number d (X) = |X| − |N(X)| is the difference of X ⊆ V , and A ∈ Ind(G) is critical if d(A) = max{d (I) : I ∈ Ind(G)} [7]. Let us recall the following definitions: ker(G) = ∩{S : S is a critical independent set} [5], core (G) = ∩{S : S is a maximum in...

The independence ratio i(G) of a graph G is the ratio of its independence number and the number of vertices. The ultimate categorical independence ratio of a graph G is defined as limk→∞ i(G×k), where G×k denotes the kth categorical power of G. This parameter was introduced by Brown, Nowakowski and Rall, who asked about its value for complete multipartite graphs. In this paper we determine the ...

Twenty-four general-practice trainees were assessed at the beginning and end of their training year. They improved significantly in their factual recall and problem-solving ability. Sixteen young principals who had had an unstructured training for general practice were assessed at the same time and were initially of the same standard but their results showed no difference over the same year.

This paper describes a system for rapidly retargetable interactive translingual retrieval. Basic functionality can be achieved for a new document language in a single day, and further improvements require only a relatively modest additional investment. We applied the techniquesfirst to searchChinese collections using English queries, and have successfully added French, German, and Italian docum...

It is proven that if G is a 3-cyclable graph on n vertices, with minimum degree δ and with a maximum independent set of cardinality α, then G contains a cycle of length at least min{n, 3δ− 3, n+ δ − α}.

Synchronization and coordination are important mechanisms involved in imitation and social interaction. In this paper, we study different methods to improve the reactivity of agents to changes in their environment in different coordination tasks. In a robot synchronization task, we compare the differences between using only position detection or velocity detection. We first test an existing pos...

Article history: Available online 8 January 2014

Let G be a graph of sufficiently large order n, and let a and b be integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑x∈e h(e) ≤ b holds for any x ∈ V (G), then G[Fh] is called a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) | h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (simply, fractional ID-[a, b]-facto...