Abstract
We introduce a notion of bipartite minors and prove a bipartite analog of Wagner's theorem: a bipartite graph is planar if and only if it does not contain K3,3 as a bipartite minor. Similarly, we provide a forbidden minor characterization for outerplanar graphs and forests. We then establish a recursive characterization of bipartite (2, 2)-Laman graphs - a certain family of graphs that contains all maximal bipartite planar graphs.
Original language | English (US) |
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Pages (from-to) | 219-228 |
Number of pages | 10 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 116 |
DOIs | |
State | Published - Jan 2016 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
Keywords
- Bipartite graphs
- Bipartite minors
- Kuratowski's theorem
- Laman graphs
- Minors
- Peripheral cycles
- Planar and outerplanar graphs