6 papers
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…
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…
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…
Hamilton decompositions of equal-side directed tori
SangHyun Park
Let be the Cartesian product of positively oriented directed cycles of length . We prove that decomposes into directed Hamilton cycles for every $m\ge3…
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…
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…