We prove that if G = (VG, EG) is a finite, simple, and undirected graph with κ components and independence number α(G), then there exist a positive integer k ∈ N and a function f : VG → N0 with non-negative integer values such that f(u) ≤ dG(u) for u ∈ VG, α(G) ≥ k ≥ ∑ u∈VG 1 dG(u)+1−f(u) , and ∑ u∈VG f(u) ≥ 2(k − κ). This result is a best-possible improvement of a result due to Harant and Schi...

R. Klein Levinski College Tel A vi v, Israel An m-<1egel1er'a J. Schonheim School of Mathematical Sciences Sackler Faculty of Exact Sciences Tel Aviv Israel every subgraph of which has minimal at most m. An (mI, m2, ... , the set of which can be partitioned into s sets generating rpc,,,prtlvplv We conjecture that such a graph is )J colorable. Partial results is settled. ~VU"Uv',"". but not e...

We give an upper bound on the independence number of the cube of the odd cycle C8n+5. The best known lower bound is conjectured to be the truth; we prove the conjecture in the case 8n + 5 prime and, within 2, for general n.

This Teaching Case has been developed to assist students in introductory first year MIS courses to develop an understanding of business context, while building practical expertise in IS modeling techniques and problem solving. The case has been formulated around a small financial planning practice, in order to work in a learning environment where students may not have had any (or limited) expos...

Several algorithms are presented. The standard algorithm generates all N anticliques of a graph with v vertices in time O(Nv). It can be adapted to e.g. generate all maximum cardinality anticliques, or just one maximum anticlique. The latter is our main achievement and was programmed using the Mathematica 6.0 code. For a random (45, 92)-graph G a maximum anticlique of size 21 was found in 1.344...

As an easy example of divide, prune, and conquer, we give an output-sensitive O(n log k)-time algorithm to compute, for n intervals, a maximum independent set of size k.

Let X1, X2, . . . , Xn be independent random variables and Sk = Pk i=1 Xi. We show that for any constants ak, P( max 1≤k≤n ||Sk| − ak| > 11t) ≤ 30 max 1≤k≤n P(||Sk| − ak| > t). We also discuss similar inequalities for sums of Hilbert and Banach space valued random vectors.

We study the problem of estimating the number of edges in a graph with access to only an independent set oracle. Independent set queries draw motivation from group testing and have applications to the complexity of decision versus counting problems. We give two algorithms to estimate the number of edges in an n-vertex graph: one that uses only polylog(n) bipartite independent set queries, and a...

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 ...