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math.CO2026
Series-parallel extensions and Ehrhart positivity
Yao Li, Sihong Shao
We prove Ehrhart positivity for series-parallel matroids and extend this result to all series-parallel extensions of multi-path matroids. A formula for the Ehrhart coefficients of…
math.CO2025
Every 2-connected, cubic, planar graph with faces of size at most 6 is Hamiltonian
Sihong Shao, Yuxuan Wu
We prove that every 2-connected, cubic, planar graph with faces of size at most 6 is Hamiltonian, and show that the 6-face condition is tight. Our results push the connectivity con…