Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Listing All Maximal Cliques in Sparse Graphs in Near-optimal Time   The degeneracy of an $n$-vertex graph $G$ is the smallest number $d$ such
that every subgraph of $G$ contains a vertex of degree at most $d$. We show
that there exists a nearly-optimal fixed-parameter tractable algorithm for
enumerating all maximal cliques, parametrized by degeneracy. To achieve this
result, we modify the classic Bron--Kerbosch algorithm and show that it runs in
time $O(dn3^{d/3})$. We also provide matching upper and lower bounds showing
that the largest possible number of maximal cliques in an $n$-vertex graph with
degeneracy $d$ (when $d$ is a multiple of 3 and $n\ge d+3$) is $(n-d)3^{d/3}$.
Therefore, our algorithm matches the $\Theta(d(n-d)3^{d/3})$ worst-case output
size of the problem whenever $n-d=\Omega(n)$.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
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The categories of this paper are: stat
2
The categories of this paper are: math
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The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph