Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $K^{\aleph_0}$ Game: Vertex Colouring   We investigate games played between Maker and Breaker on an infinite complete
graph whose vertices are coloured with colours from a given set, each colour
appearing infinitely often. The players alternately claim edges, Makers aim
being to claim all edges of a sufficiently colourful infinite complete subgraph
and Breakers aim being to prevent this. We show that if there are only finitely
many colours then Maker can obtain a complete subgraph in which all colours
appear infinitely often, but that Breaker can prevent this if there are
infinitely many colours. Even when there are infinitely many colours, we show
that Maker can obtain a complete subgraph in which infinitely many of the
colours each appear infinitely often.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs