Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum $\Delta$-edge-colorable subgraphs of class II graphs   A graph $G$ is class II, if its chromatic index is at least $\Delta+1$. Let
$H$ be a maximum $\Delta$-edge-colorable subgraph of $G$. The paper proves best
possible lower bounds for $\frac{|E(H)|}{|E(G)|}$, and structural properties of
maximum $\Delta$-edge-colorable subgraphs. It is shown that every set of
vertex-disjoint cycles of a class II graph with $\Delta\geq3$ can be extended
to a maximum $\Delta$-edge-colorable subgraph. Simple graphs have a maximum
$\Delta$-edge-colorable subgraph such that the complement is a matching.
Furthermore, a maximum $\Delta$-edge-colorable subgraph of a simple graph is
always class I.

4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat