-циклические орграфы
Šachové úlohy v kombinatorice
Článek pojednává o matematických úlohách souvisejících se šachovnicí a šachovými figurami. Ze šachu však budeme potřebovat pouze pravidla pro pohyb figur po šachovnici. Postupně se zaměřujeme na jezdcovy procházky po obdélníkových šachovnicích a dále na tzv. nezávislost a dominanci figur a vztah mezi nimi na čtvercových šachovnicích. Ukážeme, že některé problémy lze řešit elegantněji, pokud je přeformulujeme v řeči teorie grafů.
Sachs triangulations, generated by dessins d'enfant, and regular maps
Salem numbers, Pisot numbers, Mahler measure, and graphs.
Sampling 3-colourings of regular bipartite graphs.
Satisfying states of triangulations of a convex -gon.
Saturation numbers for trees.
Saturation numbers of books.
Scale-free percolation
We formulate and study a model for inhomogeneous long-range percolation on . Each vertex is assigned a non-negative weight , where are i.i.d. random variables. Conditionally on the weights, and given two parameters , the edges are independent and the probability that there is an edge between and is given by . The parameter is the percolation parameter, while describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there...
Schälbare Cohen-Macauley-Komplexe und ihre Parametrisierung.
Schauder fixed point theorem in spaces with global nonpositive curvature.
Schur complements of matrices with acyclic bipartite graphs.
Score lists in bipartite multi hypertournaments
Score lists of oriented tripartite graphs.
Secant tree calculus
A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.
Secure domination and secure total domination in graphs
A secure (total) dominating set of a graph G = (V,E) is a (total) dominating set X ⊆ V with the property that for each u ∈ V-X, there exists x ∈ X adjacent to u such that is (total) dominating. The smallest cardinality of a secure (total) dominating set is the secure (total) domination number . We characterize graphs with equal total and secure total domination numbers. We show that if G has minimum degree at least two, then . We also show that is at most twice the clique covering number of...
Secure sets and their expansion in cubic graphs
Consider a graph whose vertices play the role of members of the opposing groups. The edge between two vertices means that these vertices may defend or attack each other. At one time, any attacker may attack only one vertex. Similarly, any defender fights for itself or helps exactly one of its neighbours. If we have a set of defenders that can repel any attack, then we say that the set is secure. Moreover, it is strong if it is also prepared for a raid of one additional foe who can strike anywhere....
Segments of score sequences.
Seidel-Equivalence in LB3 (6) Graphs.
Selberg's trace formula on the -regular tree and applications.