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Let G be a balanced bipartite graph of order 2n and minimum degree δ(G) 3. If, for every balanced independent set S of four vertices, N(S) >n then G is traceable, the circumference is at least 2n - 2 and G contains a 2-factor (with only small order exceptional graphs for the latter statement). If the neighborhood union condition is replaced by N(S) >n + 2 then G is hamiltonian.
Let G H denote the Kronecker product of graphs G and H. Principal results are as follows: (a) If m is even and n ≡ 0 (mod 4), then one component of P m+1 P n+1 , and each component of each of C m P n+1 , P m+1 C n and C m C n are edge decomposable into cycles of uniform length rs, where r and...
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