Graph Partition Problems Into Cycles And Paths

Let G be a graph of order n and k any positive integer with k2k, where k is a positive integer. Let Supposing 1.1 2/c + 2, we show that, if n > 2k, then G contains k vertex-disjoint cycles; if n - 2k, then G contains k - 1 quadrilaterals and a path of order 4 which are pair wisely vertex-disjoint. We also show that if V1 - V2 = n>2k+1 and then G contains a 2-factor with exactly k components.In addition, the author also takes part in a discussion of a sufficient condition onHamilton cycle in graphs with Yang Jin. Let G be a simple graph which has n vertices. is an H-sequence. n + K + k - 3 for each Y G (G), then G is hamiltonian.