منابع مشابه
Bicircular 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 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 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 کاملThe structure of bases in bicircular matroids
In this paper we introduce a partial order on the elements of a matroid based on its fundamental circuits. The partial order is used to define and classify fundamental and secondary equivalence classes of a bicircular matroid. These classes form the basic building blocks of bicircuLlar generalized networks, i.e., generalized networks containing no unit cycles. Here, we use the classes to analyz...
متن کاملOn the number of bases of bicircular matroids
Let t(G) be the number of spanning trees of a connected graph G, and let b(G) be the number of bases of the bicircular matroid B(G). In this paper we obtain bounds relating b(G) and t(G), and study in detail the case where G is a complete graph Kn or a complete bipartite graph Kn,m.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.12.015