proposition: Lemma kconnected_edge (G : sgraph) (k : nat) : k.+1.-connected G -> exists x y : G , x -- y.
proof: Proof. move=> k1G. have [gt1kG _] := k1G. have/card_gt0P [x _] : 0 < #|G| by apply: leq_trans gt1kG. have k_edge := kconnected_degree x k1G. have/card_gt0P [y /in_setP xy] : 0 < #|N(x)| by apply: leq_trans k_edge. by exists x,y. Qed.
imports: mathcomp(all_ssreflect) GraphTheory(edone preliminaries digraph mgraph sgraph set_tac)