Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alternating Path and Coloured Clustering   In the Coloured Clustering problem, we wish to colour vertices of an edge
coloured graph to produce as many stable edges as possible, i.e., edges with
the same colour as their ends. In this paper, we reveal that the problem is in
fact a maximum subgraph problem concerning monochromatic subgraphs and
alternating paths, and demonstrate the usefulness of such connection in
studying these problems.
  We obtain a faster algorithm to solve the problem for edge-bicoloured graphs
by reducing the problem to a minimum cut problem. On the other hand, we push
the NP-completeness of the problem to edge-tricoloured planar bipartite graphs
of maximum degree four. Furthermore, we also give FPT algorithms for the
problem when we take the numbers of stable edges and unstable edges,
respectively, as parameters.

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The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci