State space properties of finite logics
Stationary map coloring
We consider a planar Poisson process and its associated Voronoi map. We show that there is a proper coloring with 6 colors of the map which is a deterministic isometry-equivariant function of the Poisson process. As part of the proof we show that the 6-core of the corresponding Delaunay triangulation is empty. Generalizations, extensions and some open questions are discussed.
Stationary random graphs on with prescribed iid degrees and finite mean connections.
Stationary random graphs with prescribed iid degrees on a spatial Poisson process.
Statuses and branch-weights of weighted trees
In this paper we show that in a tree with vertex weights the vertices with the second smallest status and those with the second smallest branch-weight are the same.
Statuses and double branch weights of quadrangular outerplanar graphs
In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs
Steiner distance in graphs
Steiner Minimal Trees for Regular Polygons.
Steiner Minimal Trees on Sets of Four Points.
Stopping Markov processes and first path on graphs
Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a noncombinatorial method to compute the law of stopping. Several examples are presented. The problem of embedding a graph into a larger but minimal graph under some constraints is studied. Given a connected graph, we show a noncombinatorial manner to compute the law of a first given path among a set of stopping paths.We prove the existence of a minimal Markov chain without oversized information....
Straight line representations of planar graphs.
Straight-line drawings of binary trees with linear area and arbitrary aspect ratio.
Straight-line drawings on restricted integer grids in two and three dimensions.
Stratidistance in stratified graphs
A graph is a stratified graph if its vertex set is partitioned into classes (each of which is a stratum or a color class). A stratified graph with strata is -stratified. If is a connected -stratified graph with strata
Streng parametrische Bedingungen und die Anzahl ihrer nicht isomorphen Modelle.
Strict refinement for direct sums and graphs.
Strictly convex drawings of planar graphs.
Strong asymmetric digraphs with prescribed interior and annulus
The directed distance from to in a strong digraph is the length of a shortest path in . The eccentricity of a vertex in is the directed distance from to a vertex furthest from in . The center and periphery of a strong digraph are two well known subdigraphs induced by those vertices of minimum and maximum eccentricities, respectively. We introduce the interior and annulus of a digraph which are two induced subdigraphs involving the remaining vertices. Several results concerning...
Strong Chromatic Index Of Planar Graphs With Large Girth
Let Δ ≥ 4 be an integer. In this note, we prove that every planar graph with maximum degree Δ and girth at least 1 Δ+46 is strong (2Δ−1)-edgecolorable, that is best possible (in terms of number of colors) as soon as G contains two adjacent vertices of degree Δ. This improves [6] when Δ ≥ 6.
Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees
A Roman dominating function (RDF) on a graph G = (V,E) is a function f : V −→ {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF is the value f(V (G)) = P u2V (G) f(u). An RDF f in a graph G is independent if no two vertices assigned positive values are adjacent. The Roman domination number R(G) (respectively, the independent Roman domination number iR(G)) is the minimum weight of an RDF (respectively,...