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Let G be a graph of order n≥3. An even squared Hamiltonian cycle (ESHC) of G is a Hamiltonian cycle C=v1v2…vnv1 of G with chords vivi+3 for all 1≤i≤n (where vn+j=vj for j≥1). When n is even, an ESHC contains all bipartite 2-regular graphs of order n. We prove that there is a positive integer N such that for every graph G of even order n≥N, if the minimum degree is δ(G)≥n2+92, then G contains an ESHC...
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