Maximum Weighted Induced Bipartite Subgraphs and Acyclic Subgraphs of Planar Cubic Graphs

Copyright © [2016] by The Society for Industrial and Applied Mathematics. All rights reserved

We study the node-deletion problem consisting of finding a maximum weighted induced bipartite subgraph of a planar graph with maximum degree three. We show that this is polynomially solvable. It was shown in [4] that it is NP-complete if the maximum degree is four. We also extend these ideas to the problem of balancing signed graphs.

We also consider maximum weighted induced acyclic subgraphs of planar directed graphs. If the maximum degree is three, it is easily shown that this is polynomially solvable. We show that for planar graphs with maximum degree four it is NP-complete.

By: Mourad Baïou, Francisco Barahona

Published in: SIAM Journal on Discrete Mathematics, volume 30, (no 2), pages 1290-1301; 10.1137/140980053 in 2016


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