We first devise a branching algorithm that computes a minimum independent dominating set with running time O∗(1.3351n) = O∗(20.417n) and polynomial space. This improves upon the best state of the art algorithms for this problem. We then study approximation of the problem by moderately exponential time algorithms and show that it can be approximated within ratio 1 + ε, for any ε > 0, in a time s...

We study graphs in which the maximum and the minimum sizes of a maximal independent set differ by exactly one. We call these graphs almost well-covered, in analogy with the class of well-covered graphs, in which all maximal independent sets have the same size. A characterization of graphs of girth at least 8 having exactly two different sizes of maximal independent sets due to Finbow, Hartnell,...

This note consists of two rather separate topics . In §1 we generalize a topic from combinatorial number theory to get an order of magnitude for the number of elements in a maximal set of residues (mod p) such that sums of different numbers of elements from this set are distinct. We show that the correct order is ep'" 3 although we are unable to establish the correct value for the constant c . ...

We give a constructive proof using tropical modifications of the existence of a family of real algebraic plane curves with asymptotically maximal numbers of even ovals.

The aim of this note is to understand invertible modules over a commutative Salgebra in the sense of Elmendorf, Kriz, Mandell & May in some very well-behaved cases. Our main result shows that as long as the commutative S-algebra R has ‘reductions mod m’ for all maximal ideals m ⊳ R∗, and Noetherian localisations (R∗)m , then for every invertible R-module U , U∗ = π∗U is an invertible R∗-module.

Lately, explicit upper bounds on |L(1, χ)| (for primitive Dirichlet characters χ) taking into account the behaviors of χ on a given finite set of primes have been obtained. This yields explicit upper bounds on residues of Dedekind zeta functions of abelian number fields taking into account the behavior of small primes, and it as been explained how such bounds yield improvements on lower bounds ...

Let G denotes a finite abelian group of order n and Davenport constant D, and put m = n+D − 1. Let x = (x1, · · · , xm) ∈ G be a sequence with a maximal repetition l attained by xm and put r = min(D, l). Let w = (w1, · · · , wm−r) ∈ Z. Then there are an n-subset I ⊂ [1,m − r] and an injection f : I 7→ [1,m], such that m ∈ f(I) and ∑

We show that the number of maximal sum-free subsets of {1, 2, . . . , n} is at most 2. We also show that 2 is an upper bound on the number of maximal product-free subsets of any group of order n.

In the present paper we give the full description of the Lie nilpo-tent group algebras which have maximal Lie nilpotency indices.

Let E/K be an elliptic curve defined over a number field, let ĥ be the canonical height on E, and let K/K be the maximal abelian extension of K. Extending work of Baker [4], we prove that there is a constant C(E/K) > 0 so that every nontorsion point P ∈ E(K) satisfies ĥ(P ) > C(E/K).