The Highly Connected Even-Cycle and Even-Cut Matroids

Stabilizer theorems for even cut matroids

A graft is a representation of an even cut matroid M if the cycles of M correspond to the even cuts of the graft. Two, long standing, open questions regarding even cut matroids are the problem of finding an excluded minor characterization and the problem of efficiently recognizing this class of matroids. Progress on these problems has been hampered by the fact that even cut matroids can have an...

Stabilizer theorems for even cycle matroids

A signed graph is a representation of an even cycle matroid M if the cycles of M correspond to the even cycles of that signed graph. Two, long standing, open questions regarding even cycle matroids are the problem finding an excluded minor characterization and the problem of efficiently recognizing this class of matroids. Progress on these problems has been hampered by the fact that even cycle ...

On 4-connected graphs without even cycle decompositions

The even and odd cut polytopes

Deza, M. and M. Laurent, The even and odd cut polytopes, Discrete Mathematics 119 (1993) 49966. The cut polytope P, is the convex hull of the incidence vectors of all cuts of the complete graph K, on n nodes. An even cut is a cut of even cardinality. For n odd, all cuts are even. For n even, we consider the even cut polytope EvP,, defined as the convex hull of the incidence vectors of all even ...

Basis graphs of even Delta-matroids

A -matroid is a collection B of subsets of a finite set I, called bases, not necessarily equicardinal, satisfying the symmetric exchange property: For A,B ∈ B and i ∈ A B, there exists j ∈ B A such that (A {i, j}) ∈ B. A -matroid whose bases all have the same cardinality modulo 2 is called an even -matroid. The basis graph G=G(B) of an even -matroid B is the graph whose vertices are the bases o...