Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An extremal problem on potentially $K_{p_{1},p_{2},...,p_{t}}$-graphic
  sequences   A sequence $S$ is potentially $K_{p_{1},p_{2},...,p_{t}}$ graphical if it has
a realization containing a $K_{p_{1},p_{2},...,p_{t}}$ as a subgraph, where
$K_{p_{1},p_{2},...,p_{t}}$ is a complete t-partite graph with partition sizes
$p_{1},p_{2},...,p_{t} (p_{1}\geq p_{2}\geq ...\geq p_{t} \geq 1)$. Let
$\sigma(K_{p_{1},p_{2},...,p_{t}}, n)$ denote the smallest degree sum such that
every $n$-term graphical sequence $S$ with $\sigma(S)\geq
\sigma(K_{p_{1},p_{2},...,p_{t}}, n)$ is potentially
$K_{p_{1},p_{2},...,p_{t}}$ graphical. In this paper, we prove that $\sigma
(K_{p_{1},p_{2},...,p_{t}}, n)\geq
2[((2p_{1}+2p_{2}+...+2p_{t}-p_{1}-p_{2}-...-p_{i}-2)n
-(p_{1}+p_{2}+...+p_{t}-p_{i})(p_{i}+p_{i+1}+...+p_{t}-1)+2)/2]$ for $n \geq
p_{1}+p_{2}+...+p_{t}, i=2,3,...,t.$

22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ