Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cutting a tree with Subgraph Complementation is hard, except for some
  small trees   For a property $\Pi$, Subgraph Complementation to $\Pi$ is the problem to
find whether there is a subset $S$ of vertices in the input graph $G$ such that
modifying $G$ by complementing the subgraph induced by $S$ results in a graph
satisfying the property $\Pi$. We prove that, the problem of Subgraph
Complementation to $T$-free graphs is NP-Complete, for $T$ being a tree, except
for 40 trees of at most 13 vertices (a graph is $T$-free if it does not contain
any induced copies of $T$). Further, we prove that these hard problems do not
admit any subexponential-time algorithms, assuming the Exponential Time
Hypothesis. As an additional result, we obtain that Subgraph Complementation to
paw-free graphs can be solved in polynomial-time.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas