23,362 research outputs found
Comparison of matroid intersection algorithms for large circuit analysis
This paper presents two approaches to symbolic analysis of large analog integrated circuits via simplification during the generation of the symbolic expressions. Both techniques are examined from the point of view of matroid theory. Finally, a new approach which combines the positive features of both approaches is introduced
The VC-Dimension of Graphs with Respect to k-Connected Subgraphs
We study the VC-dimension of the set system on the vertex set of some graph
which is induced by the family of its -connected subgraphs. In particular,
we give tight upper and lower bounds for the VC-dimension. Moreover, we show
that computing the VC-dimension is -complete and that it remains
-complete for split graphs and for some subclasses of planar
bipartite graphs in the cases and . On the positive side, we
observe it can be decided in linear time for graphs of bounded clique-width
Binary Determinantal Complexity
We prove that for writing the 3 by 3 permanent polynomial as a determinant of
a matrix consisting only of zeros, ones, and variables as entries, a 7 by 7
matrix is required. Our proof is computer based and uses the enumeration of
bipartite graphs. Furthermore, we analyze sequences of polynomials that are
determinants of polynomially sized matrices consisting only of zeros, ones, and
variables. We show that these are exactly the sequences in the complexity class
of constant free polynomially sized (weakly) skew circuits.Comment: 10 pages, C source code for the computation available as ancillary
file
Intrinsic linking and knotting of graphs in arbitrary 3-manifolds
We prove that a graph is intrinsically linked in an arbitrary 3-manifold M if
and only if it is intrinsically linked in S^3. Also, assuming the Poincare
Conjecture, we prove that a graph is intrinsically knotted in M if and only if
it is intrinsically knotted in S^3.Comment: This is the version published by Algebraic & Geometric Topology on 9
August 200
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