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math.CO2025
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}, .…
math.CO2023
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…
math.CO2023
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…