3 problems

Let $G$ be an almost bipartite non-König–Egerváry graph, and let $C$ be its unique odd cycle. A maximum matching of $G$ is a matching with the largest possible number of edges. Lev…

Let $G$ be a finite graph. Write $ucleus(G)$ for its nucleus, $diadem(G)$ for its diadem, and $alpha(G)$ for its independence number. A graph is König–Egerváry when its independen…

Diadem–corona characterization conjecture. If