k 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 components has an Euler circuit (,each of less than m. By the inductive hypothesis. .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