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math.CO2014
Graphical representations of graphic frame matroids
Rong Chen, Matt DeVos, Daryl Funk +1
A frame matroid M is graphic if there is a graph G with cycle matroid isomorphic to M. In general, if there is one such graph, there will be many. Zaslavsky has shown that frame ma…
math.CO2014
When does a biased graph come from a group labelling?
Matt DeVos, Daryl Funk, Irene Pivotto
A biased graph consists of a graph together with a collection of distinguished cycles of , called balanced cycles, with the property that no theta subgraph contains exactly…
math.CO2014
Biased graphs with no two vertex-disjoint unbalanced cycles
Rong Chen, Irene Pivotto
Lovász has completely characterised the structure of graphs with no two vertex-disjoint cycles, while Slilaty has given a structural characterisation of graphs with no two vertex-d…