Supereulerian of regular matroids with cogirth conditions
Xiaoxiao Qin, Fangyu Zhao, Hong‐Jian Lai, Bofeng Huo · Discrete Applied Mathematics · 2025
Let G be a 2-connected simple graph on sufficiently large n vertices. Catlin proved that if δ ( G ) ≥ n 5 , then G is supereulerian. Let M be a connected simple regular matroid. Huo et al. proved that M is supereulerian if g ∗ ( M ) ≥ max { r ( M ) + 1 10 , 9 } . In this paper, we prove that a simple connected regular matroid M is supereulerian if g ∗ ( M ) ≥ max { r ( M ) + 1 10 , 8 } , or g ∗ ( M ) ≥ max { r ( M ) + 1 15 , 9 } .