Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $K_{s,t}$-saturated bipartite graphs   An $n$-by-$n$ bipartite graph is $H$-saturated if the addition of any missing
edge between its two parts creates a new copy of $H$. In 1964, Erd\H{o}s,
Hajnal and Moon made a conjecture on the minimum number of edges in a
$K_{s,s}$-saturated bipartite graph. This conjecture was proved independently
by Wessel and Bollob\'as in a more general, but ordered, setting: they showed
that the minimum number of edges in a $K_{(s,t)}$-saturated bipartite graph is
$n^2-(n-s+1)(n-t+1)$, where $K_{(s,t)}$ is the "ordered" complete bipartite
graph with $s$ vertices in the first color class and $t$ vertices in the
second. However, the very natural question of determining the minimum number of
edges in the unordered $K_{s,t}$-saturated case remained unsolved. This problem
was considered recently by Moshkovitz and Shapira who also conjectured what its
answer should be. In this short paper we give an asymptotically tight bound on
the minimum number of edges in a $K_{s,t}$-saturated bipartite graph, which is
only smaller by an additive constant than the conjecture of Moshkovitz and
Shapira. We also prove their conjecture for $K_{2,3}$-saturation, which was the
first open case.

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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th