1 research outputs found
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.Comment: 15 pages and 3 figure