Geometric hyperquasigroups and line spaces
Geometric influences II: Correlation inequalities and noise sensitivity
In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand’s lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini–Kalai–Schramm (BKS) noise sensitivity theorem....
Geometric simultaneous embeddings of a graph and a matching.
Geometric structures on toroidal maps and elliptic curves
Geometric thickness of complete graphs.
Géométrie et analyse sur les arbres
Geometrie und Kombinatorik.
Géométries combinatoires finies
Geometry and combinatorics related to vector partition functions
Geometry of links.
Giant vacant component left by a random walk in a random d-regular graph
We study the trajectory of a simple random walk on a d-regular graph with d ≥ 3 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time un, where u > 0 is a fixed positive parameter. We show that this so-called vacant set exhibits a phase transition in u in the following sense: there...
Global alliances and independence in trees
A global defensive (respectively, offensive) alliance in a graph G = (V,E) is a set of vertices S ⊆ V with the properties that every vertex in V-S has at least one neighbor in S, and for each vertex v in S (respectively, in V-S) at least half the vertices from the closed neighborhood of v are in S. These alliances are called strong if a strict majority of vertices from the closed neighborhood of v must be in S. For each kind of alliance, the associated parameter is the minimum cardinality of such...
Global alliances and independent domination in some classes of graphs.
Global defensive alliances in graphs.
Global domination and neighborhood numbers in Boolean function graph of a graph
For any graph , let and denote the vertex set and the edge set of respectively. The Boolean function graph of is a graph with vertex set and two vertices in are adjacent if and only if they correspond to two adjacent vertices of , two adjacent edges of or to a vertex and an edge not incident to it in . In this paper, global domination number, total global domination number, global point-set domination number and neighborhood number for this graph are obtained.
Glossary of signed and gain graphs and allied areas.
Glued convexity spaces, frames and graphs
Going down in (semi)lattices of finite Moore families and convex geometries
In this paper we first study what changes occur in the posets of irreducible elements when one goes from an arbitrary Moore family (respectively, a convex geometry) to one of its lower covers in the lattice of all Moore families (respectively, in the semilattice of all convex geometries) defined on a finite set. Then we study the set of all convex geometries which have the same poset of join-irreducible elements. We show that this set—ordered by set inclusion—is a ranked join-semilattice and we...
Goldberg-Coxeter construction for 3- and 4-valent plane graphs.
Good lower and upper bounds on binomial coefficients.