Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hamiltonicity of the $k$-regular graph game   We consider a game played on an initially empty graph where two players
alternate drawing an edge between vertices subject to the condition that no
degree can exceed $k$. We show that for $k=3$, either player can avoid a
Hamilton cycle, and for $k\geq4$, either player can force the resulting graph
to be Hamiltonian.

34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics