Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Analysis of a Subtraction Game on Graphs   We define a two-player combinatorial game in which players take alternate
turns; each turn consists on deleting a vertex of a graph, together with all
the edges containing such vertex. If any vertex became isolated by a player's
move then it would also be deleted. A player wins the game when the other
player has no moves available.
  We study this game under various viewpoints: by finding specific strategies
for certain families of graphs, through using properties of a graph's
automorphism group, by writing a program to look at Sprague-Grundy numbers, and
by studying the game when played on random graphs.
  When analyzing Grim played on paths, using the Sprague-Grundy function, we
find a connection to a standing open question about Octal games.

23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph