Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithm for monochromatic vertex-disconnection of graphs   Let G be a vertex-colored graph. We call a vertex cut S of G a monochromatic
vertex cut if the vertices of S are colored with the same color. The graph G is
monochromatically vertex-disconnected if any two nonadjacent vertices of G has
a monochromatic vertex cut separating them. The monochromatic
vertex-disconnection number of G, denoted by mvd(G), is the maximum number of
colors that are used to make G monochromatically vertex-disconnected. In this
paper, we propose an algorithm to compute mvd(G) and give an mvd-coloring of
the graph G. We run this algorithm with an example written in Java. The main
part of the code is shown in Appendix B and the complete code is given on
Github: https://github.com/fumiaoT/mvd-coloring.git. Secondly, inspired by the
previous localization principle, we obtain a upper bound of mvd(G) for some
special classes of graphs. In addition, when mvd(G) is large and all blocks of
G are minimally 2-connected triangle-free graphs, we characterize G. On these
bases, we show that any graph whose blocks are all minimally 2-connected graphs
of small order, can be computed mvd(G) and given an mvd-coloring in polynomial
time.

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The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int