collaborators

6 papers

math.CO2026

Short Second Proof of the Odd-Modulus Directed Torus Hamilton Decomposition Theorem

SangHyun Park

Let , with all generators oriented positively. We give a second proof that decomposes into dire…

math.SP2026

Effective Angular Asymptotics and the Sharp Horoconvex Gap Scale

SangHyun Park

We prove first-band large-diameter asymptotics for the Dirichlet spectrum on horoconvex domains in real hyperbolic space. After Chebyshev centering, a divergent sequence compactifi…

math.CO2026

Two Arc-Disjoint Hamiltonian Paths in Finite Two-Generated Abelian Cayley Digraphs

SangHyun Park

We prove the finite abelian two-generator conjecture of Darijani--Miraftab--Witte Morris: every directed Cayley digraph on a finite abelian group with two distinct nonzero generato…

math.CO2026

Hamilton decompositions of all directed tori at odd modulus

SangHyun Park

Let denote the directed Cayley graph on the positive coordinate basis, equivalently the Cartesian produc…

math.CO2026

Hamilton decompositions of the directed 5-torus for odd modulus

SangHyun Park

We prove that the directed five-dimensional torus has a Hamilton decomposition for every odd integer $m…

math.CO2026

Hamilton decompositions of the directed 3-torus: a return-map and odometer view

SangHyun Park

We prove that the directed 3-torus D_3(m), or equivalently the Cartesian product of three directed m-cycles, admits a decomposition into three arc-disjoint directed Hamilton cycles…