Примеры использования Forbidden minors на Английском языке и их переводы на Русский язык
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These seven graphs form the forbidden minors for linklessly embeddable graphs,
then F has bounded local treewidth if and only if one of the forbidden minors for F is an apex graph.
the minimal forbidden minors are a two-edge path graph
therefore that there are additional forbidden minors for the YΔY-reducible graphs.
One of the finitely many forbidden minors characterizing F is planar; F is a minor-closed
Any other graph G is an apex graph if and only if none of the forbidden minors is a minor of G. These forbidden minors include the seven graphs of the Petersen family,
for which every cycle basis is weakly fundamental can be characterized by five forbidden minors: the graph of the square pyramid,
These graphs are forbidden minors for F: a graph belongs to F if and only if it
nevertheless the matroids with any finite bound on their branchwidth have finitely many minimal forbidden minors, all of which have a number of elements that is at most exponential in the branchwidth.
The Wagner graph is also one of four minimal forbidden minors for the graphs of treewidth at most three(the other three being the complete graph K5, the graph of the regular octahedron, and the graph of the pentagonal prism) and one of four minimal forbidden minors for the graphs of branchwidth at most three the other three being K5,
For k 1, the unique forbidden minor is a 3-vertex cycle graph.
For k 2, the unique forbidden minor is the 4-vertex complete graph K4.
For the partial 2-trees the single forbidden minor is the complete graph on four vertices.
This graph family may be characterized by a single forbidden minor.
The existence of forbidden minor characterizations for all minor-closed graph families is an equivalent way of stating the Robertson-Seymour theorem.
Y-Δ reducible graphs, the forbidden minor characterizations of both classes, and the connection to planar partial 3-trees are all from El-Mallah& Colbourn 1990.
The Robertson-Seymour theorem implies that an analogous forbidden minor characterization exists for every property of graphs that is preserved by deletions
The forbidden minor characterization of linkless graphs leads to a polynomial time algorithm for their recognition, but not for actually constructing an embedding.
Each of the Petersen family graphs forms a minimal forbidden minor for the family of YΔY-reducible graphs.
A graph is a forbidden minor for this property if it has no planar cover,