Eulerian and bipartite binary delta-matroids
Combinatorics
2020-03-05 v1
Abstract
Delta-matroid theory is often thought of as a generalization of topological graph theory. It is well-known that an orientable embedded graph is bipartite if and only if its Petrie dual is orientable. In this paper, we first introduce the concepts of Eulerian and bipartite delta-matroids and then extend the result from embedded graphs to arbitrary binary delta-matroids. The dual of any bipartite embedded graph is Eulerian. We also extend the result from embedded graphs to the class of delta-matroids that arise as twists of binary matroids. Several related results are also obtained.
Keywords
Cite
@article{arxiv.2003.02125,
title = {Eulerian and bipartite binary delta-matroids},
author = {Qi Yan and Xian'an Jin},
journal= {arXiv preprint arXiv:2003.02125},
year = {2020}
}
Comments
13 pages, 0 figures. arXiv admin note: text overlap with arXiv:1602.01306, arXiv:1403.0920 by other authors