Las Vergnas–Meyniel quasi-minor conjecture

Let $K_t$ denote the complete graph on $t$ vertices. A quasi-$K_t$-minor in a graph $G$ consists of $t$ nonempty, pairwise disjoint vertex sets $B_1,\ldots,B_t$ such that each union $B_i\cup B_j$ induces a connected subgraph for every distinct $i,j$; a $K_t$-minor additionally requires each individual $B_i$ to induce a connected subgraph. Las Vergnas–Meyniel's Conjecture C. For any $t$, any graph that admits a quasi-$K_t$-minor admits a $K_t$-minor. The paper presents this conjecture among the claims disproved by its construction.