General bounds for identifying codes in some infinite regular graphs.
Generalizations of Parikh mappings
Parikh matrices have become a useful tool for investigation of subword structure of words. Several generalizations of this concept have been considered. Based on the concept of formal power series, we describe a general framework covering most of these generalizations. In addition, we provide a new characterization of binary amiable words – words having a common Parikh matrix.
Generalized golden ratios of ternary alphabets
Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in dependence...
Generalized Lyndon words. (Mots de Lyndon généralisés.)
Generalized pascal triangles: overview of new results
Generalized Thue-Morse words and palindromic richness
We prove that the generalized Thue-Morse word defined for and as , where denotes the sum of digits in the base- representation of the integer , has its language closed under all elements of a group isomorphic to the dihedral group of order consisting of morphisms and antimorphisms. Considering antimorphisms , we show that is saturated by -palindromes up to the highest possible level. Using the generalisation of palindromic richness recently introduced by the author and E. Pelantová,...
Generating functions for permutations which contain a given descent set.
Generating functions for Wilf equivalence under generalized factor order.
Generátory pseudonáhodných čísel založené na nekonečných slovech
Geometric thickness of complete graphs.
Graph colorings with local constraints - a survey
We survey the literature on those variants of the chromatic number problem where not only a proper coloring has to be found (i.e., adjacent vertices must not receive the same color) but some further local restrictions are imposed on the color assignment. Mostly, the list colorings and the precoloring extensions are considered. In one of the most general formulations, a graph G = (V,E), sets L(v) of admissible colors, and natural numbers for the vertices v ∈ V are given, and the question is whether...
Graph decompositions and factorizing permutations.
Graph drawing by high-dimensional embedding.
Graph fibrations, graph isomorphism, and PageRank
PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the...
Graph layout aesthetics in UML diagrams: User preferences.
Graphes canoniques de graphes algébriques
Graphes sans circuit et bilinéarité
Graphs of low chordality.
Gray codes for -free strings.
Gray-ordered binary necklaces.