Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On induced saturation for paths   For a graph $H$, a graph $G$ is $H$-induced-saturated if $G$ does not contain
an induced copy of $H$, but either removing an edge from $G$ or adding a
non-edge to $G$ creates an induced copy of $H$. Depending on the graph $H$, an
$H$-induced-saturated graph does not necessarily exist. In fact, Martin and
Smith (2012) showed that $P_4$-induced-saturated graphs do not exist, where
$P_k$ denotes a path on $k$ vertices. Axenovich and Csik\'{o}s (2019) asked the
existence of $P_k$-induced-saturated graphs for $k \ge 5$; it is easy to
construct such graphs when $k\in\{2, 3\}$. Recently, R\"{a}ty constructed a
graph that is $P_6$-induced-saturated. In this paper, we show that there exists
a $P_{k}$-induced-saturated graph for infinitely many values of $k$. To be
precise, we find a $P_{3n}$-induced-saturated graph for every positive integer
$n$. As a consequence, for each positive integer $n$, we construct infinitely
many $P_{3n}$-induced-saturated graphs. We also show that the Kneser graph
$K(n,2)$ is $P_6$-induced-saturated for every $n\ge 5$.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th