Bipartite induced subgraphs and well-quasi-ordering

Korpelainen, Nicholas and Lozin, Vadim V. (2011). Bipartite induced subgraphs and well-quasi-ordering. Journal of Graph Theory, 67(3) pp. 235–249.

DOI: https://doi.org/10.1002/jgt.20528

Abstract

We study bipartite graphs partially ordered by the induced subgraph relation. Our goal is to distinguish classes of bipartite graphs that are or are not well-quasi-ordered (wqo) by this relation. Answering an open question from [J Graph Theory 16 (1992), 489–502], we prove that P7-free bipartite graphs are not wqo. On the other hand, we show that P6-free bipartite graphs are wqo. We also obtain some partial results on subclasses of bipartite graphs defined by forbidding more than one induced subgraph

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