Geodesic
Cobiased graphs: single-element extensions and elementary quotients of graphic matroids
Daniel Slilaty1 ; Thomas Zaslavsky2
1Wright State University
2Department of Mathematics and Statistics, Binghamton University, Binghamton, New York, USA
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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Zaslavsky (1991) introduced a graphical structure called a biased graph and used it to characterize all single-element coextensions and elementary lifts of graphic matroids. We introduce a new graphical structure that we call a cobiased graph and use it to characterize single-element extensions and elementary quotients of graphic matroids.
DOI : 10.37236/12148
Classification : 05B35, 05C22, 52B40
Mots-clés : biased graph, quotients of graphic matroids

Daniel Slilaty  1   ; Thomas Zaslavsky  2

1 Wright State University
2 Department of Mathematics and Statistics, Binghamton University, Binghamton, New York, USA 
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Daniel Slilaty; Thomas Zaslavsky. Cobiased graphs: single-element extensions and elementary quotients of graphic matroids. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12148

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