This paper develops necessary and sufficient conditions for the existence of Hamiltonian paths in rectangular grid graphs with triangular holes by decomposing the graph into structured subgraphs and applying parity and geometric constraints. Download pdf

This report systematically enumerates and analyzes Hamiltonian paths in small rectangular grid graphs with constrained endpoint positions, using exhaustive generation, symmetry-aware counting, and structural decompositions to derive recurrence relations—particularly for 3×n grids. Download pdf

This document presents a detailed case-by-case construction framework for Hamiltonian paths in rectangular grid graphs with T-shaped holes, explicitly showing how valid paths can be assembled from Hamiltonian paths and cycles on carefully defined subgraphs. Download pdf