I.1 Connected Components
... Simple graphs. The abstract concept of a graph is a pair G = (V, E) consisting of set of vertices, V , and a set of edges, E, each a pair of vertices. We draw the vertices as points or little circles and edges as line segments or curves connecting the points. Crossings between curves are allowed as ...
... Simple graphs. The abstract concept of a graph is a pair G = (V, E) consisting of set of vertices, V , and a set of edges, E, each a pair of vertices. We draw the vertices as points or little circles and edges as line segments or curves connecting the points. Crossings between curves are allowed as ...
Math 8301, Manifolds and Topology Homework 8 1. Show that S
... 1. Show that S 2 is isomorphic to the universal covering space of RP2 . 2. Give a description of the universal cover of the space S 2 ∨ S 1 , obtained by gluing together S 2 and S 1 at a single point. 3. Suppose X and Y are path-connected spaces, p : Y → X is a covering map, and y ∈ Y . Let the imag ...
... 1. Show that S 2 is isomorphic to the universal covering space of RP2 . 2. Give a description of the universal cover of the space S 2 ∨ S 1 , obtained by gluing together S 2 and S 1 at a single point. 3. Suppose X and Y are path-connected spaces, p : Y → X is a covering map, and y ∈ Y . Let the imag ...
PDF
... The notation f : X ,→ Y is often used for embeddings. The embeddings correspond to the subspaces. Observe that f and the inclusion map of the subspace f [X] into X differ only up to a homeomorphism. ...
... The notation f : X ,→ Y is often used for embeddings. The embeddings correspond to the subspaces. Observe that f and the inclusion map of the subspace f [X] into X differ only up to a homeomorphism. ...
Topological embeddings of graphs in graphs
... NONEMBEDDING EXAMPLE. If E is a graph homeomorphic to a Figure Eight and T is a graph homeomorphic to a Figure Theta, then neither is homeomorphic to a subspace of the other. The proof of this assertion has two parts. One uses the local homology groups at points which are defined in Section VII.1 of ...
... NONEMBEDDING EXAMPLE. If E is a graph homeomorphic to a Figure Eight and T is a graph homeomorphic to a Figure Theta, then neither is homeomorphic to a subspace of the other. The proof of this assertion has two parts. One uses the local homology groups at points which are defined in Section VII.1 of ...
k-ordered
... A graph is said to be k-cyclable if given any set of k vertices, there is a cycle that contains the k vertices. (introduced in 1967) It is well known that being 2-connected is equivalent to being 2-cyclable,and that in general being k-connected implies k-cyclable. Also, a hamiltonian graph is one t ...
... A graph is said to be k-cyclable if given any set of k vertices, there is a cycle that contains the k vertices. (introduced in 1967) It is well known that being 2-connected is equivalent to being 2-cyclable,and that in general being k-connected implies k-cyclable. Also, a hamiltonian graph is one t ...