Alternating connectivity of tournaments
Alternating cycles and realizations of a degree sequence
Altitude of wheels and wheel-like graphs
An edge-ordering of a graph G=(V, E) is a one-to-one mapping f:E(G)→{1, 2, ..., |E(G)|}. A path of length k in G is called a (k, f)-ascent if f increases along the successive edges forming the path. The altitude α(G) of G is the greatest integer k such that for all edge-orderings f, G has a (k, f)-ascent. In our paper we give exact values of α(G) for all helms and wheels. Furthermore, we use our result to obtain altitude for graphs that are subgraphs of helms.
Amalgamations and link graphs of Cayley graphs.
Amenability, unimodularity, and the spectral radius of random walks on finite graphs.
Amenable group actions on infinite graphs.
Amenable groups and cellular automata
We show that the theorems of Moore and Myhill hold for cellular automata whose universes are Cayley graphs of amenable finitely generated groups. This extends the analogous result of A. Machi and F. Mignosi “Garden of Eden configurations for cellular automata on Cayley graphs of groups” for groups of sub-exponential growth.
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...
Amply regular graphs and block designs.
An algebraic characterization of geodetic graphs
We say that a binary operation is associated with a (finite undirected) graph (without loops and multiple edges) if is defined on and if and only if , and for any , . In the paper it is proved that a connected graph is geodetic if and only if there exists a binary operation associated with which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).
An algebraic framework of weighted directed graphs.
An algorithm for optimal partitioning of a graph
An Algorithm for Scaling Matrices and Computing the Minimum Cycle Mean in a Digraph.
An algorithm to construct greedy drawings of triangulations.
An Algorithm To Recognize A Generalized Line Graph And Output It's Root Graph
An algorithmic Friedman-Pippenger theorem on tree embeddings and applications.
An almost naive algorithm for finding relative neighbourhood graphs in metrics
An alternative construction of normal numbers
A new class of -adic normal numbers is built recursively by using Eulerian paths in a sequence of de Bruijn digraphs. In this recursion, a path is constructed as an extension of the previous one, in such way that the -adic block determined by the path contains the maximal number of different -adic subblocks of consecutive lengths in the most compact arrangement. Any source of redundancy is avoided at every step. Our recursive construction is an alternative to the several well-known concatenative...
An analogon of the fixed-point theorem and its application for graphs
An anti-Ramsey condition on trees.