An Erdős-Gallai conjecture (Q1068106)

The following conjecture (1966) of P. Erdős and T. Gallai is confirmed: Every graph on n vertices can be covered by n-1 circuits and edges. A slightly stronger form of the planar case of this conjecture was formerly proved by Tao Mao-qi, Shen Yun-qiu and Ku Tung-shin (preprint), stating that every 2-edge-connected planar graph can be covered by n-2 circuits. The present paper gives a shorter proof. In addition, two other related results are also established.