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arXiv · 1801.06494

Quasimonotone graphs

Martin Dyer·Haiko Müller
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Abstract

For any class $\mathcal{C}$ of bipartite graphs, we define quasi-$\cal C$ to be the class of all graphs $G$ such that every bipartition of $G$ belongs to $\cal C$. This definition is motivated by a generalisation of the switch Markov chain on perfect matchings from bipartite graphs to nonbipartite graphs. The monotone graphs, also known as bipartite permutation graphs and proper interval bigraphs, are such a class of bipartite graphs. We investigate the structure of quasi-monotone graphs and hence construct a polynomial time recognition algorithm for graphs in this class.

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Martin Dyer, Haiko Müller. 2018-01-19. Quasimonotone graphs. https://arxiv.org/abs/1801.06494

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