# Gale-Ryser型刻划定理的一个推广A Generalization of the Gale-Ryser Type Characterization Theorem

Abstract: Let and be two non-increasing sequences of nonnegative integers. The pair is said to be bigraphic if there is a simple X,Y-bigraph such that the vertices of X have degrees and the vertices of Y have degrees . is said to be t-bigraphic if it is bigraphic and no two vertices from different partite sets are joined by more than t edges. In this paper, we give a characterization for to be t-bigraphic. In fact, it is a gen-eration of the Gale-Ryser type characterization theorem.

[1] Gale, D. (1957) A Theorem on Flows in Networks. Pacific Journal of Mathematics, 7, 1073-1082.
http://dx.doi.org/10.2140/pjm.1957.7.1073

[2] Ryser, H.J. (1957) Combinatorial Properties of Matrices of Zeros and Ones. Canada Journal of Mathematics, 9, 371-377.
http://dx.doi.org/10.4153/CJM-1957-044-3

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