Related papers: End-transitive graphs
A self-contained account of the theory of structure trees for edge cuts in networks is given. Applications include a generalisation of the Max-Flow Min-Cut Theorem to infinite networks and a short proof of a conjecture of Kropholler. This…
We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.
In this paper we further develop the theory of one sided shift spaces over infinite alphabets, characterizing one-step shifts as edge shifts of ultragraphs and partially answering a conjecture regarding shifts of finite type (we show that…
We show that the topological space of any infinite graph and its ends is normal. In particular, end spaces themselves are normal.
Let $G$ be a $p$-group. We begin to consider the relationship between the structure of the commuting graph and $|G:Z(G)|$. We also build a family of groups whose commuting graphs have more than one connected component whose diameter is at…
Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we determine conditions under which such a separation system contains a nested…
We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…
We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.
Structural balance theory assumes triads in networks to gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for considering…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
A detour in a graph is a longest path. This thesis is mainly about connected, non-traceable graphs with the property that each vertex is the start (or end) vertex of a detour. There are also related results on claw-free, 2-connected,…
We study topological properties of the graph topology.
In this paper we study the structure of the graphs associated with the iterations of the map $x \mapsto x+x^{-1}$ over finite fields of characteristic three.
We prove a refinement of the tree packing theorem by Tutte/Nash-Williams for finite graphs. This result is used to obtain a similar result for end faithful spanning tree packings in certain infinite graphs and consequently to establish a…
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…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
Given two graphs, a mapping between their edge-sets is cycle-continuous, if the preimage of every cycle is a cycle. The motivation for this notion is Jaeger's conjecture that for every bridgeless graph there is a cycle-continuous mapping to…
We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…