4 papers · 1 filter
Edge-disjoint linkage in infinite graphs
Amena Assem, R. Bruce Richter
In 1980, Thomassen stated his weak linkage conjecture: for an odd positive integer k, if a graph G is k-edge-connected, then, for any collection of k pairs of vertices {s_1,t_1}, .…
Towards Nash-Williams Orientation Conjecture for Infinite Graphs
Amena Assem
In 1960 Nash-Williams proved that an edge-connectivity of 2k is sufficient for a finite graph to have a k-arc-connected orientation. He then conjectured that the same is true for i…
Analysis of the Lifting Graph
Amena Assem
The `lifting` or `splitting-off` operation on graphs is performed by deleting two edges sv and sw having a common end s and adding a new edge between v and w. Such a lift is consid…
The Nash-Williams orientation theorem for graphs with countably many ends
Amena Assem, Marcel Koloschin, Max Pitz
Nash-Williams proved in 1960 that a finite graph admits a -arc-connected orientation if and only if it is -edge-connected, and conjectured that the same result should hold f…