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. The theory of graph minors began with Wagner's theorem that a graph is planar if and only if its minors include neither the complete graph K5 nor the complete bipartite graph K3,3. [1]

A graph is a minor of a graph if a copy of can be obtained from via repeated edge deletion and/or edge contraction. The Kuratowski reduction theorem states that any nonplanar graph has the complete graph or the complete bipartite graph as a minor.

In graph theory, the Robertson–Seymour theorem (also called the graph minor theorem[1]) states that the undirected graphs, partially ordered by the graph minor relationship, form a well-quasi-ordering. [2]

graph H is a minor of a graph G if H can be obtained from vertices and edges and contracting edges. We say that G contains. H, if a graph isomorphic to H is a minor of G. It is easy to see that the minor relation is transitive, that is if G H and H F then G F .

A minor of a graph G is a graph obtained from G by contracting edges, deleting edges, and deleting isolated vertices; a proper minor of G is any minor other than G itself.

Apr 8, 2025 · The Robertson-Seymour theorem, also called the graph minor theorem, is a generalization of the Kuratowski reduction theorem by Robertson and Seymour, which states that the collection of finite graphs is well-quasi-ordered by minor embeddability, from which it follows that Kuratowski's "forbidden minor" embedding obstruction generalizes to ...

A graph G can be embedded in the plane (is planar) if and only if neither the com-plete graph K5 nor the complete bipar-tite graph K3,3 is a minor of G. In topology, this theorem is usually expressed in an equivalent form saying that no subgraph of G is homeomorphic to K5 or K3,3.

Oct 24, 2005 · simple but important graph properties that are minor closed (inherited by minors). Being cycle-free (i.e., a forest) is one. Being series-parallel is a more complicated example: these are graphs that can be obtained from a single edge by a sequence of parallel .

Jun 6, 2020 · Let $ G $ be a graph (possibly with loops and multiple edges). A minor of $ G $ is any graph obtained by a succession of the following operations: i) deletion of a single edge; ii) contraction of a single edge; iii) removal of an isolated vertex. The graph minor theorem of N. Robertson and P.D. Seymour says the following.

A graph H is a minor of a graph G, if H can be obtained from G by deleting and contracting edges, and deleting isolated vertices. Many important classes of graphs are closed under minors, in the sense that if G belongs to the class then so does any minor of G. Examples are the class of planar graphs, or more generally the graphs embeddable in ...