Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs with the Erdos-Ko-Rado property   For a graph G and integer r \geq 1 we denote the family of independent r-sets
of V(G) by I^{(r)}(G). A graph G is said to be r-EKR if no intersecting
subfamily of I^{(r)}(G) is larger than the largest such family all of whose
members contain some fixed v \in V(G). If this inequality is always strict,
then G is said to be strictly r-EKR. We show that if a graph G is r-EKR then
its lexicographic product with any complete graph is r-EKR.
  For any graph G, we define \mu(G) to be the minimum size of a maximal
independent vertex set. We conjecture that, if 1 \leq r \leq 1/2\mu(G), then G
is r-EKR, and if r<1/2\mu(G), then G is strictly r-EKR. This is known to be
true when G is an empty graph, a cycle, a path or the disjoint union of
complete graphs. We show that it is also true when G is the disjoint union of a
pair of complete multipartite graphs.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom