mathematics, topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological...

crossing). A topological graph is also called a drawing of a graph. An important special class of topological graphs is the class of geometric graphs, where...

arrow head. Minor (graph theory) Edge contraction Archdeacon, Dan (1996), "Topological graph theory: a survey", Surveys in graph theory (San Francisco, CA...

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it...

the mathematical field of graph theory, a toroidal graph is a graph that can be embedded on a torus. In other words, the graph's vertices and edges can be...

topological graphs, where the edges are allowed to be arbitrary continuous curves connecting the vertices; thus, it can be described as "the theory of...

that the graph can be drawn without crossing itself on a sphere with n cross-caps or on a sphere with n/2 handles. In topological graph theory there are...

In topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional...

of a topological space is an important topological invariant, the zeroth Betti number, the number of components of a graph is an important graph invariant...

In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation...

graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is...

mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...

In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges, vertices and by contracting edges...

puzzle can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph K 3 , 3 {\displaystyle K_{3,3}} , with...

plane drawing of a given graph, as a function of the number of edges and vertices of the graph. It states that, for graphs where the number e of edges...

number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the...

parts of topology, e.g. knot theory. Algebraic graph theory has close links with group theory and topological graph theory has close links to topology...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing...

(born November 30, 1938) is a mathematician working mainly in topological graph theory, currently a distinguished professor emeritus at the Ohio State...

In topological graph theory, a ribbon graph is a way to represent graph embeddings, equivalent in power to signed rotation systems and graph-encoded maps...

The same definition applies to any topological space which has a finitely generated homology. Given a topological space which has a finitely generated...

Connectedness is one of the principal topological properties that distinguish topological spaces. A subset of a topological space X {\displaystyle X} is a connected...

In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies...

discrete Morse theory. Sperner's lemma Discrete exterior calculus Topological graph theory Combinatorial topology Finite topological space de Longueville...

whole graph be reachable from the root vertex. In topological graph theory, the notion of a rooted graph may be extended to consider multiple vertices or...

Gross, J. L.; Alpert, S. R. (1974). "The topological theory of current graphs". Journal of Combinatorial Theory, Series B. 17 (3): 218–233. doi:10...

In graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are...

plane. For the coloring to exist, the graph must be bipartite. The faces of the embedding are required to be topological disks. The surface and the embedding...

In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles. They were discovered...