Quasi‐graphic matroids* |
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| Authors: | Jim Geelen Bert Gerards Geoff Whittle |
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| Affiliation: | 1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada;2. Centrum Wiskunde and Informatica, Amsterdam, The Netherlands;3. School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, New ZealandCorrespondence Jim Geelen, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada. Email: |
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| Abstract: | Frame matroids and lifted‐graphic matroids are two interesting generalizations of graphic matroids. Here, we introduce a new generalization, quasi‐graphic matroids, that unifies these two existing classes. Unlike frame matroids and lifted‐graphic matroids, it is easy to certify that a 3‐connected matroid is quasi‐graphic. The main result is that every 3‐connected representable quasi‐graphic matroid is either a lifted‐graphic matroid or a frame matroid. |
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| Keywords: | frame matroids graphic matroids matroids representation 05B35 |
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