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Everything about Graph minor
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting edges. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Graph minorA 5-minute orientation
- Skim a recent paper: Graph product structure for non-minor-closed classesInfluential work since 2022
- Pick up a classic book: Writing ArgumentsThe most-reprinted book on the subject
- Read the landmark paper: Minor-embedding in adiabatic quantum computation: II. Minor-universal graph designCited 248 times
- Go sideways: Hadwiger conjecture (graph theory)A closely related topic
- Go sideways: Klaus WagnerA closely related topic
đź“– Definitions
Noun A graph which can be formed from some specified graph by performing vertex deletions, edge deletions, and edge contractions on the specified graph.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
Diameter and Treewidth in Minor-Closed Graph Families
Graph minor theory
Excluding any graph as a minor allows a low tree-width 2-coloring
Coloring the square of a K4-minor free graph
Graph Minor Approach for Application Mapping on CGRAs
Layered separators in minor-closed graph classes with applications
Systematic and deterministic graph minor embedding for Cartesian products of graphs
🆕 Influential since 2022
Graph product structure for non-minor-closed classes
k -apices of Minor-closed Graph Classes. II. Parameterized Algorithms
Local certification of graph decompositions and applications to minor-free classes
k-apices of minor-closed graph classes. I. Bounding the obstructions
The graph minor theorem in topological combinatorics
đź“š Books worth reading
Writing ArgumentsJohn D. Ramage, John C. Bean · 2000
An introduction to computer scienceJean-Paul Tremblay, Richard B. Bunt · 1979
GraphentheorieReinhard Diestel · 1997- 📕Topics in structural graph theoryLowell W. Beineke, Robin J. Wilson · 2012
Thirty Essays on Geometric Graph TheoryJános Pach · 2012
Drupal 7 bibleRic Shreves · 2011- 📕Topics in topological graph theoryLowell W. Beineke, Robin J. Wilson · 2009
Graph theoryReinhard Diestel · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Hadwiger conjecture (graph theory) Unsolved problem in mathematics Does every graph with chromatic number k have a k-vertex complete graph as a minor? More unsolved problems in mathematics…
- Klaus Wagner Klaus Wagner (March 31, 1910 – February 6, 2000) was a German mathematician known for his contributions to graph theory. Wagner studied topology at the…
- Graph structure theorem In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between…
- Hadwiger number In graph theory, the Hadwiger number of an undirected graph G is the size of the largest complete graph that can be obtained by contracting edges of G…
- Branch-decomposition In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree…
- Apex graph In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called…
- Linkless embedding In topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional…
- Paul Seymour (mathematician) Paul D. Seymour FRS (born 1950) is a British mathematician known for his work in discrete mathematics, especially graph theory. He (with others) was responsible…