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 all directed tori at odd modulus
SangHyun Park
Let denote the directed Cayley graph on the positive coordinate basis, equivalently the Cartesian produc…
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…