A characterization of the graphic split-off matroids
نویسندگان
چکیده
We consider the problem of determining precisely which graphs G have the property that the split-off operation, by every pair of edges, on the cycle matroid M(G) yields a graphic matroid. This problem is solved by proving that there are exactly four minor-minimal graphs that do not have this property.
منابع مشابه
Base exchange properties of graphic matroids
New base exchange properties of binary and graphic matroids are derived. The graphic matroids within the class of 4-connected binary matroids are characterized by base exchange properties. Some progress with the characterization of arbitrary graphic matroids is made. Characterizing various types of matroids by base exchange properties is e.g. important in invariant theory.
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 کاملForbidden-minor characterization for the class of graphic element splitting matroids
This paper is based on the element splitting operation for binary matroids that was introduced by Azadi as a natural generalization of the corresponding operation in graphs. In this paper, we consider the problem of determining precisely which graphic matroids M have the property that the element splitting operation, by every pair of elements on M yields a graphic matroid. This problem is solve...
متن کاملThe signed-graphic representations of wheels and whirls
We characterize all of the ways to represent the wheel matroids and whirl matroids using frame matroids of signed graphs. The characterization of wheels is in terms of topological duality in the projective plane and the characterization of whirls is in terms of topological duality in the annulus.
متن کاملOn cographic matroids and signed-graphic matroids
We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph Σ iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that Σ must be the projective-planar dual signed graph of an actual imbedding of G in the projective plane. As a corollary we get that, if G1, . . . , G29 denote the 29 nonseparable forbidden minors for projective-pl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 50 شماره
صفحات -
تاریخ انتشار 2011