Short proofs of two theorems are given: (i) Whitney's 2-isomorphism theorem characterizing all graphs with the same cycle matroid, and (ii) Tutte's excluded minor characterization of those binary matroids that are graphic. Graph connectivity plays an important role in both proofs.
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On theorems of Whitney and Tutte. 151 of odd degree, it follows that in every graph 2-isomorphic to G/f, P-{f} has at least four vertices of odd degree, a ...
Our goal here is to prove analogues of theorems of Whitney and Tutte in this new setting. For a 2-regular digraph H embedded in a surface S, we define a Whitney.
Theorem 7 (Tutte, 1966). A 3-connected matroid M has an element e such that M\e or M/e is 3-connected unless M has rank at least three and is a whirl or the ...
Duration: 15:47
Posted: Sep 3, 2022
Posted: Sep 3, 2022
The Tutte-Whitney polynomials play a key role in the study of counting problems on graphs, and have close connections with statistical mechanics and knot theory ...
Whitney's 2-isomorphism theorem states that G may be transformed to a graph G* isomorphic to H by repeated application of a simple operation, which we will ...
The Tutte polynomial has several equivalent definitions. It is essentially equivalent to Whitney's rank polynomial, Tutte's own dichromatic polynomial and ...
The Tutte-Whitney polynomials play a key role in the study of counting problems on graphs, and have close connections with statistical mechanics and knot ...
Dec 1, 2016 · Any Ck≥1 atlas of a topological manifold contains a C∞ atlas. What exactly the theorem says? Can one elaborate a little bit on this?
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