4 papers
math.CO2026
Signs of Hamiltonian Circles in Simple Plane Signed Graphs
Xiyong Yan
We study which signs can occur among Hamiltonian circles in simple plane signed graphs. Using a face-based viewpoint, we relate the sign of a Hamiltonian circle to the product of t…
math.CO2025
Realization and classification of Hamiltonian-circle multisigns
Xiyong Yan
We investigate the multisigns of Hamiltonian circles in the multisigned complete graph \(Σ_n := (K_n, Ï, \mathbb{F}_2^m)\). The \emph{multisign} of a circle \(C\) is defined as t…
math.CO2025
Double signs of Hamiltonian circles in doubly signed complete graphs
Xiyong Yan
We study Hamiltonian circles in the doubly signed complete graph . A circle's double sign is defined as the sum of its edge labels. I establish co…
math.CO2025
Hamiltonian Cycles in Signed and Multisigned Complete Graphs
Xiyong Yan
A signed complete graph contains both positive and negative Hamiltonian cycles if and only if it also contains both positive and negative triangles. Otherwise, all Hamiltonian cycl…