论文信息 - Bipartite induced subgraphs and well‐quasi‐ordering

Bipartite induced subgraphs and well‐quasi‐ordering

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. Copyright © 2011 John Wiley Periodicals, Inc. J Graph Theory 67: 235-249, 2011

Vadim V. Lozin | Nicholas Korpelainen | V. Lozin | N. Korpelainen

[1] Peter Damaschke,et al. Induced subgraphs and well-quasi-ordering , 1990, J. Graph Theory.

[2] V. Giakoumakis,et al. Bi-complement Reducible Graphs , 1997 .

[3] A. Brandstädt,et al. Graph Classes: A Survey , 1987 .

[4] Gábor Rudolf,et al. Minimal Universal Bipartite Graphs , 2007, Ars Comb..

[5] Paul D. Seymour,et al. Graph Minors. XX. Wagner's conjecture , 2004, J. Comb. Theory B.

[6] B. Mohar,et al. Graph Minors , 2009 .

[7] A. Tucker,et al. A structure theorem for the consecutive 1's property☆ , 1972 .

[8] Vassilis Giakoumakis,et al. Bipartite Graphs Totally Decomposable by Canonical Decomposition , 1999, Int. J. Found. Comput. Sci..

[9] Marko Petkovsek,et al. Letter graphs and well-quasi-order by induced subgraphs , 2002, Discret. Math..

[10] Guoli Ding,et al. Subgraphs and well-quasi-ordering , 1992, J. Graph Theory.