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Finding the interacting pairs of proteins between two different protein families whose members are known to interact is an important problem in molecular biology. We developed and tested an algorithm that finds optimal matches between two families of proteins by comparing their distance matrices. A distance matrix provides a measure of the sequence… (More)

We say (n, e) → (m, f), an (m, f) subgraph is forced, if every n-vertex graph of size e has an m-vertex spanned subgraph with f edges. For example, as Turán proved, (n, e) → " k, ` k 2 ´ " for e > t k−1 (n) and (n, e) → " k, ` k 2 ´ " , otherwise. We give a number of constructions showing that forced pairs are rare. Using tools of extremal graph theory we… (More)

1. INTRODUCTION II [1] two of us iivestigated the problem of determiiiig those cardiials a, /3, y, 8, A for which the followiig statemeet, abbreviated Iá(8, g, a, A, y), holds : "Wheeever V is aa a-dimeesiooal vector space over a field of A elemeets, aad the 8-dimeesiooal subspaces of V are partitiooed iito y classes, there is some /-dimeesiooal subspace of… (More)