About recognizing (&agr; &bgr;) classes of polar graphs
Discrete Mathematics
SIAM Journal on Discrete Mathematics
Discrete Applied Mathematics
Discrete Applied Mathematics
Combinatorial Algorithms
Recognizing line-polar bipartite graphs in time O(n)
Discrete Applied Mathematics
Recognizing polar planar graphs using new results for monopolarity
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Polar permutation graphs are polynomial-time recognisable
European Journal of Combinatorics
Algorithms for unipolar and generalized split graphs
Discrete Applied Mathematics
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A graph is polar if the vertex set can be partitioned into A and B in such a way that the subgraph induced by A is a complete multipartite graph and the subgraph induced by B is a disjoint union of cliques. Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. However, recognizing polar graphs is an NP-complete problem in general. This led to the study of the polarity of special classes of graphs such as cographs and chordal graphs, cf. Ekim et al. (2008) [7,5]. In this paper, we study the polarity of line graphs and call a graph line-polar if its line graph is polar. We characterize line-polar bipartite graphs in terms of forbidden subgraphs. This answers a question raised in the fist reference mentioned above. Our characterization has already been used to develop a linear time algorithm for recognizing line-polar bipartite graphs, cf. Ekim (submitted for publication) [6].