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 balanced submatroids in random subsets of projective geometries
Strictly convex drawings of planar graphs.
Strings with maximally many distinct subsequences and substrings.
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,...
Strong products of ?-critial graphs.
Strong products of ?-critical graphs. (Summary).
Strong sequences and the weight of regular spaces
It will be shown that if in a family of sets there exists a strong sequence of the length then this family contains a subfamily consisting of pairwise disjoint sets. The method of strong sequences will be used for estimating the weight of regular spaces.
Strong sequences, binary families and Esenin-Volpin's theorem
One of the most important and well known theorem in the class of dyadic spaces is Esenin-Volpin's theorem of weight of dyadic spaces. The aim of this paper is to prove Esenin-Volpin's theorem in general form in class of thick spaces which possesses special subbases.
Strong Transfinite Version of König's Duality Theorem.
Strong ƒ-Star Factors of Graphs
Let G be a graph and f : V (G) → {2, 3, . . .}. A spanning subgraph F is called strong f-star of G if each component of F is a star whose center x satisfies degF (x) ≤ ƒ(x) and F is an induced subgraph of G. In this paper, we prove that G has a strong f-star factor if and only if oddca(G − S) ≤ ∑x∊S ƒ(x) for all S ⊂ V (G), where oddca(G) denotes the number of odd complete-cacti of G.
Stronger bounds for generalized degrees and Menger path systems
For positive integers d and m, let denote the property that between each pair of vertices of the graph G, there are m internally vertex disjoint paths of length at most d. For a positive integer t a graph G satisfies the minimum generalized degree condition δₜ(G) ≥ s if the cardinality of the union of the neighborhoods of each set of t vertices of G is at least s. Generalized degree conditions that ensure that is satisfied have been investigated. In particular, it has been shown, for fixed positive...
Strongly cancellative and recovering sets on lattices.
Strongly geodesically automatic groups are hyperbolic.
Strongly invertible knots, rational-fold branched coverings, and hyperbolic spatial graphs.