Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lune -- Free Knot Graphs   This paper is an exploration of simple four-regular graphs in the plane (i.e.
loopless and with no more than one edge between any two nodes). Such graphs are
fundamental to the theory of knots and links in three dimensional space, and
their planar diagrams. We dedicate this paper to Frank Harary (1921 -- 2005)
whose fascination with graphs of knots inspired this work and with whom we had
the pleasure of developing this paper. We prove that for v (the number of
nodes) greater than or equal to 8 there always exist such knot-graphs. Our
proof gives rise to a class of "tight" graphs that do not submit to the
recursive procedure that generates graphs with v+2 nodes from "admissible"
graphs with v nodes. We then classify such tight graphs.

37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th