Topic
Graph minor
About: Graph minor is a research topic. Over the lifetime, 1605 publications have been published within this topic receiving 41371 citations. The topic is also known as: graph minor & minor.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: Wagner's conjecture is proved, that for every infinite set of finite graphs, one of its members is isomorphic to a minor of another.
1,098 citations
TL;DR: It is proved that for every planar graph H there is a number w such that every graph with no minor isomorphic to H can be constructed from graphs with at most w vertices, by piecing them together in a tree structure.
976 citations
TL;DR: It is proved that for any fixed planar graph H, every planar graphs with sufficiently large tree-width has a minor isomorphic to H.
920 citations
TL;DR: Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(√n) vertices, and this separator theorem in combination with a divide-and-conquer strategy leads to many new complexity results for planar graphs problems.
Abstract: Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only $O(\sqrt n )$ vertices. This separator theorem, in combination with a divide-and-conquer strategy, leads to many new complexity results for planar graph problems. This paper describes some of these results.
795 citations
TL;DR: It is proved that there is a numberk such that every graph with no minor isomorphic toH has path-width≆k, and this implies that ifP is any property of graphs such that some forest does not have propertyP, then the set of minor-minimal graphs without propertyP is finite.
716 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2024 | 2 |
| 2023 | 15 |
| 2022 | 19 |
| 2021 | 12 |
| 2020 | 16 |