Block allocation of a sequential resource

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An H -packing of G is a collection of vertex-disjoint subgraphs of G such that each component is isomorphic to H . An H -packing of G is maximal if it cannot be extended to a larger H -packing of G . In this paper we consider problem of random allocation of a sequential resource into blocks of m consecutive units and show how it can be successfully modeled in terms of maximal P m -packings. We enumerate maximal P m -packings of P n of a given cardinality and determine the asymptotic behavior of the enumerating sequences. We also compute the expected size of m -packings and provide a lower bound on the efficiency of block-allocation.