2025/06/18 by Leonardo Martínez-Sandoval, Martínez-Sandoval, Leonardo, Kolja Knauer +1
Engineering · Materials Science · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Porphyrin and Phthalocyanine Chemistry #Supramolecular Self-Assembly in Materials #Surface Chemistry and Catalysis
paper · pdf · doi:10.48550/arxiv.2506.15049
openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
There has been wide interest in understanding which properties of base graphs of matroids extend to base-cobase graphs of matroids. A significant result of Naddef and Pulleyblank (1984) shows that the 1-skeleton of any (0,1)-polytope is either a hypercube, or Hamiltonian-connected, i.e. there is a Hamiltonian path connecting any two vertices. In particular, this is true for base graphs of matroids. A natural question raised by Farber, Richter, and Shank (1985) is whether this extends to base-cobase graphs. First, we use the polytopal approach to show Hamiltonian connectivity of base-cobase graphs of series-parallel extensions of lattice path matroids. On the other hand, we show that this method extends to only very special classes related to identically self-dual matroids. Second, we show that base-cobase graphs of wheels and whirls are Hamiltonian connected. Last, we show that the regular matroid R10 yields a negative answer to the question of Farber, Richter, and Shank.