Given a digraph D=(V, A), with vertex set V and arc set A, a set S⊆ V is a dominating set if
for every vertex v in V\S, there are a vertex u in S and an arc (u, v) from u to v. In this chapter …

Governments at all scales regularly face the question: With a limited budget, which public-
good projects—eg, building bike paths or installing streetlamps—should they fund? To make …

A very nice result of Bárány and Lehel asserts that every finite subset X or R d can be
covered by h (d) X-boxes (ie each box has two antipodal points in X). As shown by Gyárfás …

The orientable domination number, DOM (G), of a graph G is the largest domination number
over all orientations of G. In this paper, DOM is studied on different product graphs and …

In this paper, we introduce the problem of finding an orientation of a given undirected graph
that maximizes the burning number of the resulting directed graph. We show that the …

In most of the world's democracies, policy decisions are primarily made by elected political
officials. However, under mounting dissatisfaction with representative government due to …

A fundamental question in social choice theory and multi-agent systems is how to aggregate
individual agents' preferences to make a prudent collective decision. A promising line of …

For a set X and a nonempty subset Y of X, denote by T (X) the full transformation semigroup
under the composition whose elements are functions on X. Let Fix (X, Y) be the …

Erd\H {o} s [On Sch\" utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $
n $ vertices has a directed dominating set of at most $\log (n+ 1) $ vertices, where $\log $ is …

The main purpose of the thesis was to exhibit sufficient conditions on digraphs to find
subdivisions of complex structures. While this type of question is pretty well understood in …