Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On upper bounds for parameters related to construction of special
  maximum matchings   For a graph $G$ let $L(G)$ and $l(G)$ denote the size of the largest and
smallest maximum matching of a graph obtained from $G$ by removing a maximum
matching of $G$. We show that $L(G)\leq 2l(G),$ and $L(G)\leq (3/2)l(G)$
provided that $G$ contains a perfect matching. We also characterize the class
of graphs for which $L(G)=2l(G)$. Our characterization implies the existence of
a polynomial algorithm for testing the property $L(G)=2l(G)$. Finally we show
that it is $NP$-complete to test whether a graph $G$ containing a perfect
matching satisfies $L(G)=(3/2)l(G)$.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci