A set S of vertices of a graph G is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number t(G) is the minimum cardinality of a total dominating set of G. Let G be a connected spanning subgraph of Ks;s, and let H be the complement of G relative to Ks;s; that is, Ks;s = G ⊕ H is a factorization of Ks;s. The graph G is k-supercritical relative...

Teichmüller’s classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given point of the domain to another given point of the domain. For a domain D ⊂ Rn , n ≥ 2 , we consider the class of all Kquasiconformal maps of D onto itself with...

The problem we want to handle in this p a p e r is vagueness. A notion of space, which we basically have, plays an important part in the faculty of thinking and speech. In this paper, we concentrate on a particular class of spatial descriptions, namely descriptions about positional relations on a two-dimensional space. A theoretical device we present in this paper is called the potential model ...

Has the MIS discipline matured enough to be considered a paradigm? This paper will review the MIS discipline from its inception, arguing that the discipline was created by what Thomas Kuhn would call a revolution leading to a paradigm shift. Using Kuhnian philosophy, the paper will argue that the MIS discipline has now reached a point to be considered a paradigm, according to the standards set ...

This article offers a set of guidelines to assist project leaders when managing virtual project teams. The guidelines were developed as a result of a panel at the celebration of the 30 anniversary of the founding of the MIS department at the University of Arizona. These guidelines include recommendations for addressing challenges that occur over the virtual team project life cycle, including id...

Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V \ S. The restrained domination number of G, denoted by γr(G), is the minimum cardinality of a restrained dominating set of G. A set S ⊆ V is a total dominating set if every vertex in V is adjacent to a vertex in S. The total domination number of a graph...

A total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. We show that given a graph of order n with minimum degree at least 2, one can add at most (n−2√n )/4+O(log n) edges such that the resulting graph has two disjoint total dominating sets, and this bound is best possible.

(Note that for circuits we implicitly assume that ∅ / ∈ C(M), just as we assume that for matroids ∅ ∈ I.) Proof: 1. follows from the definition that a circuit is a minimally dependent set, and therefore a circuit cannot contain another circuit. 2. Let X, Y ∈ C(M) where X 6= Y , and e ∈ X ∩ Y . From 1, it follows that X \ Y is non-empty; let f ∈ X \ Y . Assume on the contrary that (X ∪ Y ) − e i...

For any field F, the set of all functions f : V (G) → F whose sum on each maximal independent set is constant forms a vector space over F. In this paper, we show that the dimension can vary depending on the characteristic of the field. We also investigate the dimensions of these vector spaces and show that while some families, such as chordal graphs, have unbounded dimension, other families, su...