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 fi...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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12171402,12101600)by the Fundamental Research Funds for the Central Universities(No.2021QN1037)。
文摘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.
