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...

graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor...

family and further exclude all graphs from the family which contain any of these forbidden graphs as (induced) subgraph or minor. A prototypical example of...

In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations...

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 graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect...

establishes a deep and fundamental connection between the theory of graph minors and topological embeddings. The theorem is stated in the seventeenth...

mathematics Does every graph with chromatic number k {\displaystyle k} have a k {\displaystyle k} -vertex complete graph as a minor? More unsolved problems...

In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three...

bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the...

In graph theory, a shallow minor or limited-depth minor is a restricted form of a graph minor in which the subgraphs that are contracted to form the minor...

In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space ⁠ R n {\displaystyle \mathbb {R}...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

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...

complete graph K6, the Petersen graph, and the other five graphs in the Petersen family do not have linkless embeddings. Every graph minor of a linklessly...

YΔY-reducible graphs, and relations between treewidth and graph diameter. Apex graphs are closed under the operation of taking minors: contracting any...

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...

drawing. Outerplanar graphs may be characterized (analogously to Wagner's theorem for planar graphs) by the two forbidden minors K4 and K2,3, or by their...

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...

embeddable graphs as the graphs with μ ≤ 4 and as the graphs with no Petersen family minor. For k = 5 the set of forbidden minors includes the 78 graphs of the...

restriction and contraction operations. Matroid minors are closely related to graph minors, and the restriction and contraction operations by which they are formed...

that a finite graph is planar if and only if its minors include neither K5 (the complete graph on five vertices) nor K3,3 (the utility graph, a complete...

In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest...

number h(G) is the largest number n for which the complete graph Kn is a minor of G, a smaller graph obtained from G by edge contractions and vertex and edge...

Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De...

graphs, and characterizing the ends and clique minors of infinite graphs. If G is an undirected graph, and X is a set of vertices, then an X-flap is a...

graph from an initial one by a complex change, such as: transpose graph; complement graph; line graph; graph minor; graph rewriting; power of graph;...

In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first...

In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique...

for all graphs, both of these numbers are within a constant factor of each other, and both quantities may be characterized by forbidden minors. And as...