Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterising and recognising game-perfect graphs   Consider a vertex colouring game played on a simple graph with $k$
permissible colours. Two players, a maker and a breaker, take turns to colour
an uncoloured vertex such that adjacent vertices receive different colours. The
game ends once the graph is fully coloured, in which case the maker wins, or
the graph can no longer be fully coloured, in which case the breaker wins. In
the game $g_B$, the breaker makes the first move. Our main focus is on the
class of $g_B$-perfect graphs: graphs such that for every induced subgraph $H$,
the game $g_B$ played on $H$ admits a winning strategy for the maker with only
$\omega(H)$ colours, where $\omega(H)$ denotes the clique number of $H$.
Complementing analogous results for other variations of the game, we
characterise $g_B$-perfect graphs in two ways, by forbidden induced subgraphs
and by explicit structural descriptions. We also present a clique module
decomposition, which may be of independent interest, that allows us to
efficiently recognise $g_B$-perfect graphs.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: stat
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci