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The <i>exponent of matrix multiplication</i> is the smallest real number &#969; such that for all &#949;&gt;0, <i>O</i>(n<sup>&#969;+&#949;</sup>) arithmetic operations suffice to multiply two <i>n&#215;n</i> matrices. The standard algorithm for matrix multiplication shows that &#969;&#8804;3. Strassen's remarkable result [5] shows that &#969;&#8804;2.81,(More)
We define a distance of two graphs that reflects the closeness of both local and global properties. We also define convergence of a sequence of graphs, and show that a graph sequence is convergent if and only if it is Cauchy in this distance. Every convergent graph sequence has a limit in the form of a symmetric measurable function in two variables. We use(More)
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency conditions, and normalized, multiplica-tive and reflection positive graph parameters. In this paper we show that each of these(More)
Matroids allowing an odd ear decomposition can be viewed as natural generalizations of factor-critical graphs. We show that a matroid representable over a eld of characteristic 2 allows an odd ear decomposition if and only if it can be represented by a space on which the induced scalar product is a nondegenerate symplectic form. We will also show that for a(More)