Block Additivity of ℤ2-Embeddings
نویسندگان
چکیده
Westudy embeddings of graphs in surfaces up toZ2-homology. We introduce a notion of genus mod 2 and show that some basic results, mostnoteworthyblock additivity, hold forZ2-genus.Thishas consequences for (potential) Hanani-Tutte theorems on arbitrary surfaces.
منابع مشابه
Block Additivity of Z2-Embeddings
We study embeddings of graphs in surfaces up to Z2-homology. We introduce a notion of genus mod 2 and show that some basic results, most noteworthy block additivity, hold for Z2-genus. This has consequences for (potential) Hanani-Tutte theorems on arbitrary surfaces.
متن کاملThree-page Encoding and Complexity Theory for Spatial Graphs
For each n ≥ 2, we construct a finitely presented semigroup RSGn. The center of RSGn encodes uniquely up to rigid ambient isotopy in R 3 all non-oriented spatial graphs with vertices of degree ≤ n. This encoding is obtained by using threepage embeddings of graphs into the product Y = T × I, where T is the cone on three points, and I ≈ [0, 1] is the unit segment. By exploiting three-page embeddi...
متن کاملAn Algebraic Framework for Cipher Embeddings
In this paper we discuss the idea of block cipher embeddings and consider a natural algebraic framework for such constructions. In this approach we regard block cipher state spaces as algebras and study some properties of cipher extensions on larger algebras. We apply this framework to some well-known examples of AES embeddings.
متن کاملAdditivity of maps preserving Jordan $eta_{ast}$-products on $C^{*}$-algebras
Let $mathcal{A}$ and $mathcal{B}$ be two $C^{*}$-algebras such that $mathcal{B}$ is prime. In this paper, we investigate the additivity of maps $Phi$ from $mathcal{A}$ onto $mathcal{B}$ that are bijective, unital and satisfy $Phi(AP+eta PA^{*})=Phi(A)Phi(P)+eta Phi(P)Phi(A)^{*},$ for all $Ainmathcal{A}$ and $Pin{P_{1},I_{mathcal{A}}-P_{1}}$ where $P_{1}$ is a nontrivial projection in $mathcal{A...
متن کاملLabeling Subgraph Embeddings and Cordiality of Graphs
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$. For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...
متن کامل