3 papers
math.CO2026
Eigenvalue bounds for distance-edge colorings
Aida Abiad, Harper Reijnders
For a fixed positive integer , we consider the graph colouring problem in which edges at distance at most are given distinct colours. We obtain sharp lower bounds for the di…
math.CO2026
The edge-isoperimetric number of graphs and their powers: approaches from spectral graph theory, optimization and finite geometry
Aida Abiad, Nils van de Berg, Emanuel Juliano +4
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph p…
math.CO2025
Improved Gilbert-Varshamov bound for sum-rank-metric codes via graph theory
Aida Abiad, Harper Reijnders, Michael Tait
We use a graph-theoretic approach which yields improvements on the known Gilbert-Varshamov (GV) bound for sum-rank-metric codes for certain parameters. In particular, we show that…