Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bipartite Tur\'an problems for ordered graphs   A zero-one matrix $M$ contains a zero-one matrix $A$ if one can delete some
rows and columns of $M$, and turn some 1-entries into 0-entries such that the
resulting matrix is $A$. The extremal number of $A$, denoted by $ex(n,A)$, is
the maximum number of $1$-entries in an $n\times n$ sized matrix $M$ that does
not contain $A$.
  A matrix $A$ is column-$t$-partite (or row-$t$-partite), if it can be cut
along the columns (or rows) into $t$ submatrices such that every row (or
column) of these submatrices contains at most one $1$-entry. We prove that if
$A$ is column-$t$-partite, then
$ex(n,A)<n^{2-\frac{1}{t}+\frac{1}{2t^{2}}+o(1)}$, and if $A$ is both column-
and row-$t$-partite, then $ex(n,A)<n^{2-\frac{1}{t}+o(1)}$. Our proof combines
a novel density-increment-type argument with the celebrated dependent random
choice method.
  Results about the extremal numbers of zero-one matrices translate into
results about the Tur\'an numbers of bipartite ordered graphs. In particular, a
zero-one matrix with at most $t$ 1-entries in each row corresponds to a
bipartite ordered graph with maximum degree $t$ in one of its vertex classes.
Our results are partially motivated by a well known result of F\"uredi (1991)
and Alon, Krivelevich, Sudakov (2003) stating that if $H$ is a bipartite graph
with maximum degree $t$ in one of the vertex classes, then
$ex(n,H)=O(n^{2-\frac{1}{t}})$. The aim of the present paper is to establish
similar general results about the extremal numbers of ordered graphs.

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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas