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math.CO2026
Edge-addition monotonicity of positive p-energy fails for every p >= 1
Koyar Afrasyab
At a 2021 AIM workshop, Guo conjectured that the positive square energy s+ = E+_2 should inherit the familiar edge-addition monotonicity of the spectral radius, rho(G + uv) >= rho(…
math.CO2026
A 50-Vertex Cubic Counterexample to the Domination-versus-Edge-Domination Conjecture
Koyar Afrasyab
Baste, Furst, Henning, Mohr, and Rautenbach conjectured that every finite regular graph of positive degree satisfies \(γ(G) \leq γ_e(G)\), where \(γ\) is the domination number and…
math.CO2026
Exact Zarankiewicz Values On Two Finite Frontier Slices
Koyar Afrasyab
The Zarankiewicz number Z(m,n,s,t) is the maximum number of edges in a bipartite graph with parts of orders m and n containing no copy of Ks,t. We give one combined, certificate-ba…