$\theta$-free matching covered graphs: characterization and consequences

Rohinee Joshi, Santhosh Raghul, Ajit A. Diwan +1

The Ear Decomposition Theorem of Lovász & Plummer (1986) implies that every matching covered graph (MCG), except $K_2$ and cycles, contains (at least) one of $\theta$ and $K_4$ as a con…