منابع مشابه
Handle slides for delta-matroids
A classic exercise in the topology of surfaces is to show that, using handle slides, every disc-band surface, or 1-vertex ribbon graph, can be put in a canonical form consisting of the connected sum of orientable loops, and either non-orientable loops or pairs of interlaced orientable loops. Motivated by the principle that ribbon graph theory informs delta-matroid theory, we find the delta-matr...
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Two further equivalent axioms are given for valuations of a matroid. Let M = (V,B) be a matroid on a finite set V with the family of bases B. For ω : B → R the following three conditions are equivalent: (V1) ∀B,B′ ∈ B, ∀u ∈ B −B′,∃v ∈ B′ −B: ω(B) + ω(B′) ≤ ω(B − u+ v) + ω(B′ + u− v); (V2) ∀B,B′ ∈ B with B 6= B′, ∃u ∈ B −B′,∃v ∈ B′ −B: ω(B) + ω(B′) ≤ ω(B − u+ v) + ω(B′ + u− v); (V3) ∀B,B′ ∈ B, ∀...
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J. Makowsky and B. Zilber (2004) showed that many variations of graph colorings, called CP-colorings in the sequel, give rise to graph polynomials. This is true in particular for harmonious colorings, convex colorings, mcct-colorings, and rainbow colorings, and many more. N. Linial (1986) showed that the chromatic polynomial χ(G;X) is #P-hard to evaluate for all but three values X = 0, 1, 2, wh...
متن کاملIsotropical linear spaces and valuated Delta-matroids
The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an n×n skewsymmetric matrix. Its points correspond to n-dimensional isotropic subspaces of a 2n-dimensional vector space. In this paper we tropicalize this picture, and we develop a combinatorial theory of tropical Wick vectors and tropical linear spaces that are tropically isotropic. We characterize ...
متن کاملDelta-Matroids, Jump Systems, and Bisubmodular Polyhedra
We relate an axiomatic generalization of matroids, called a jump system, to poly-hedra arising from bisubmodular functions. Unlike the case for usual submodularity, the points of interest are not all the integral points in the relevant polyhedron, but form a subset of them. However, we do show that the convex hull of the set of points of a jump system is a bisubmodular polyhedron, and that the ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2017
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2016.07.002