Related papers: Transitivity conditions in infinite graphs

We give a characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems. This characterization may be thought as a graph analog of Mostow's rigidity theorem for hyperbolic manifolds. This…

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…

Jamison and Sprague defined a graph $G$ to be a $k$-threshold graph with thresholds $\theta_1 , \ldots, \theta_k$ (strictly increasing) if one can assign real numbers $(r_v)_{v \in V(G)}$, called ranks, such that for every pair of vertices…

We analyze the number of ends of the mapping class group of a stable avenue surface. We prove that the mapping class group is one-ended whenever the stable avenue surface has at least one end of discrete type. Our method is to show that the…

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…

We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.

The orbit graph of a k-orbit polytope is a graph on k nodes that shows how the flag orbits are related by flag adjacency. Using orbit graphs, we classify k-orbit polytopes and determine when a k-orbit polytope is i-transitive. We then…

A graph of order $n$ is $p$-factor-critical, where $p$ is an integer of the same parity as $n$, if the removal of any set of $p$ vertices results in a graph with a perfect matching. 1-Factor-critical graphs and 2-factor-critical graphs are…

This paper considers how many conjugacy classes of reflections a map can have, under various transitivity conditions. It is shown that for vertex- and for face-transitive maps there is no restriction on their number or size, whereas…

This paper proposes that common measures for network transitivity, based on the enumeration of transitive triples, do not reflect the theoretical statements about transitivity they aim to describe. These statements are often formulated as…

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…

We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the…

The vertices of a $k$-token graph of a graph $G$ correspond to $k$ indistinguishable tokens placed on $k$ different vertices of $G$. Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex…

If we are given a connected finite graph $G$ and a subset of its vertices $V_{0}$, we define a distance-residual graph as a graph induced on the set of vertices that have the maximal distance from $V_{0}$. Some properties and examples of…

In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class $\mathcal{G}$, we are concerned with the maximum subclass and the minimum superclass of $\mathcal{G}$ that…

A graph $\Ga$ is $G$-symmetric if $\Ga$ admits $G$ as a group of automorphisms acting transitively on the set of vertices and the set of arcs of $\Ga$, where an arc is an ordered pair of adjacent vertices. In the case when $G$ is…

Aldous [1] asked whether every graph in which the distribution of the return time of random is independent of the starting vertex must be transitive. We remark that this question can be reduced into a purely graph-theoretic one that had…

We prove two characterisations of accessibility of locally finite quasi-transitive connected graphs. First, we prove that any such graph $G$ is accessible if and only if its set of separations of finite order is an ${\rm Aut}(G)$-finitely…

A graph is called {\em half-arc-transitive} if its full automorphism group acts transitively on vertices and edges, but not on arcs. It is well known that for any prime $p$ there is no tetravalent half-arc-transitive graph of order $p$ or…