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Quasi‐graphic matroids *
Author(s) -
Geelen Jim,
Gerards Bert,
Whittle Geoff
Publication year - 2018
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22177
Subject(s) - matroid , graphic matroid , combinatorics , generalization , mathematics , frame (networking) , discrete mathematics , computer science , mathematical analysis , telecommunications
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.