Bicircular matroids representable over GF(4) or GF(5)
نویسندگان
چکیده
منابع مشابه
Bicircular matroids representable over GF(4) or GF(5)
Given a bicircular matroid B(G) and q ∈ {4, 5}, we characterize when the bicircular matroid B(G) is GF (q)-representable by precisely describing the structure of G. These descriptions yield polynomial-time algorithms with input G to certify if B(G) is or is not GF (q)-representable.
متن کاملRepresentations of bicircular matroids
Coullard, C.R., J.G. de1 Greco and D.K. Wagner, Representations of bicircular matroids, Discrete Applied Mathematics 32 (1991) 223-240. A bicircular matroid is a matroid defined on the edge set of a graph. Two different graphs can have the same bicircular matroid. The first result of this paper is a characterization of the collection of graphs having the same bicircular matroid as a given arbit...
متن کاملBicircular matroids are 3-colorable
Hugo Hadwiger proved that a graph that is not 3-colorable must have a K4minor and conjectured that a graph that is not k-colorable must have a Kk+1minor. By using the Hochstättler-Nešetřil definition for the chromatic number of an oriented matroid, we formulate a generalized version of Hadwiger’s conjecture that might hold for the class of oriented matroids. In particular, it is possible that e...
متن کاملRepresentations of Bicircular Lift Matroids
Bicircular lift matroids are a class of matroids defined on the edge set of a graph. For a given graph G, the circuits of its bicircular lift matroid are the edge sets of those subgraphs of G that contain at least two cycles, and are minimal with respect to this property. The main result of this paper is a characterization of when two graphs give rise to the same bicircular lift matroid, which ...
متن کاملOn pancyclic representable matroids
Bondy proved that an n-vertex simple Hamiltonian graph with at least n2/4 edges has cycles of every length unless it is isomorphic to Kn/2,n/2. This paper considers finding circuits of every size in GF (q)-representable matroids with large numbers of elements. A consequence of the main result is that a rank-r simple binary matroid with at least 2r−1 elements has circuits of all sizes or is isom...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2016.03.017