Isotropic Matroids II: Circle Graphs
نویسندگان
چکیده
We present several characterizations of circle graphs, which follow from Bouchet’s circle graph obstructions theorem.
منابع مشابه
Excluding a bipartite circle graph from line graphs
We prove that for fixed bipartite circle graph H, all line graphs with sufficiently large rank-width (or clique-width) must contain an isomorphic copy of H as a pivotminor. To prove this, we introduce graphic delta-matroids. Graphic delta-matroids are minors of delta-matroids of line graphs and they generalize graphic or cographic matroids.
متن کاملTutte-martin polynomials and orienting vectors of isotropic systems
Isotropic systems are structures which unify some properties of 4-regular graphs and of pairs of dual binary matroids. In this paper we unify the properties of the symmetric Tutte polynomials (i.e. with equal variables) of binary matroids and of the Martin polynomials of 4-regular graphs. For this purpose we introduce the orienting vectors of an isotropic system in order to generalize the euler...
متن کاملIsotropic Matroids I: Multimatroids and Neighborhoods
Several properties of the isotropic matroid of a looped simple graph are presented. Results include a characterization of the multimatroids that are associated with isotropic matroids and several ways in which the isotropic matroid of G incorporates information about graphs locally equivalent to G. Specific results of the latter type include a characterization of graphs that are locally equival...
متن کاملStructural properties of fuzzy graphs
Matroids are important combinatorial structures and connect close-lywith graphs. Matroids and graphs were all generalized to fuzzysetting respectively. This paper tries to study connections betweenfuzzy matroids and fuzzy graphs. For a given fuzzy graph, we firstinduce a sequence of matroids from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matro...
متن کاملEnergy of Graphs, Matroids and Fibonacci Numbers
The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 23 شماره
صفحات -
تاریخ انتشار 2016