$$\text{C}_6\text{H}_{12}\text{O}_6 \xrightarrow{\text{HI}, \, \Delta} \text{n-hexane} \quad (\text{Proves open straight 6-carbon chain})$$
Concept: When glucose is prolonged-heated with concentrated hydroiodic acid ($$\text{HI}$$) in the presence of red phosphorus (or simply heated with $$\text{HI}$$), all hydroxyl groups ($$\text{--OH}$$) and the carbonyl carbon ($$\text{--CHO}$$) undergo complete reductive deoxygenation. This yields n-hexane, a straight six-carbon alkane.