The degree of ≤m tive hypothesis ed. h has l components, The degree of every vertex of components is even and the number of edges less than m. By the inductive hypothesis, each of components has an Euler circuit. H .G is connected❖ If E(G)=E(C), the result holds ❖ If E(G)-E(C), Let H=G-C, The degree of every vertex of H is even and e(H)m ❖ ①If H is connected, by the inductive hypothesis, H has an Euler circuit C1， ❖ C=(v0 , v1 ,…,vk-1 , v0 ) ❖ ② When H is not connected, H has l components, The degree of every vertex of components is even and the number of edges less than m. By the inductive hypothesis,each of components has an Euler circuit. Hi ❖ G is connected