An El-Zahár Type Condition Ensuring Path-Factors

Let G be a connected n-order graph and suppose that n = n 1 + \Delta \Delta \Delta + n k where n i 2 are integers. The following will be proved : If G has minimum degree at least \Xi 1 2 n 1 \Pi + \Delta \Delta \Delta + \Xi 1 2 n k \Pi then G has a spanning subgraph which consists of paths of orders n 1 ; : : : ; n k