Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fat-triangle linkage and kite-linked graphs   For a multigraph $H$, a graph $G$ is $H$-linked if every injective mapping
$\phi: V(H)\to V(G)$ can be extended to an $H$-subdivision in $G$. We study the
minimum connectivity required for a graph to be $H$-linked. A $k$-fat-triangle
$F_k$ is a multigraph with three vertices and a total of $k$ edges. We
determine a sharp connectivity requirement for a graph to be $F_k$-linked. In
particular, any $k$-connected graph is $F_k$-linked when $F_k$ is connected. A
kite is the graph obtained from $K_4$ by removing two edges at a vertex. As a
nontrivial application of $F_k$-linkage, we then prove that every $8$-connected
graph is kite-linked, which shows that the required connectivity for a graph to
be kite-linked is $7$ or $8$.

34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio