2 citations · 3 across the 8 of their papers we have counts for
7 papers · 1 filter
Tree-cut decompositions for displaying undominated edge-ends
Max Pitz, Lucas Real
We prove that every graph admits a linked, componental, rooted tree-cut decomposition of finite adhesion that displays all undominated edge-ends. As a first application, we deduce…
On tree-decompositions for infinite chordal graphs
Max Pitz, Lucas Real, Roman Schaut
A graph is chordal if it contains no induced cycle of length four or more. While finite chordal graphs are precisely those admitting tree-decompositions into cliques, this fails fo…
On order-compatible paths in infinite graphs
Max Pitz, Lucas Real, Roman Schaut
Two paths in a graph are order-compatible if their common vertices occur in the same order when travelling from to . Suppose a graph contains an infinite number…
Remarks on the countable case of the Unfriendly Partition Problem
Leandro Fiorini Aurichi, Lucas Real
The Unfriendly Partition Problem asks whether it is possible to split the vertex set of an infinite graph into two parts so that every vertex has at least as many neighbors in…
Topological remarks on end and edge-end spaces
Leandro Fiorini Aurichi, Paulo Magalhães Júnior, Lucas Real
The notion of ends in an infinite graph might be modified if we consider them as equivalence classes of infinitely edge-connected rays, rather than equivalence classes of infin…
Edge-connectivity between edge-ends of infinite graphs
Leandro Fiorini Aurichi, Lucas Real
In infinite graph theory, the notion of ends, first introduced by Freudenthal and Jung for locally finite graphs, plays an important role when generalizing statements from finite g…
Unfriendly partitions when avoiding vertices of finite degree
Leandro Fiorini Aurichi, Lucas Real
An unfriendly partition of a graph is a function such that for every vertex , where…