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Everything about Map graph
Intersection graph representing regions on the Euclidean plane
In graph theory, a branch of mathematics, a map graph is an undirected graph formed as the intersection graph of finitely many simply connected and internally disjoint regions of the Euclidean plane. The map graphs include the planar graphs, but are more general. Any number of regions can meet at a common corner, and when they do the map graph will contain a clique connecting the corresponding vertices, unlike planar graphs in which the largest cliques have only four vertices. Another example of a map graph is the king's graph, a map graph of the squares of the chessboard connecting pairs of squares between which the chess king can move. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Map graphA 5-minute orientation
- Skim a recent paper: Graph attention network with Granger causality map for fault detection and root cause diagnosisInfluential work since 2022
- Pick up a classic book: Graph coloring problemsThe most-reprinted book on the subject
- Read the landmark paper: Microbial biogeography: putting microorganisms on the mapCited 2,569 times
- Go sideways: BidimensionalityA closely related topic
- Go sideways: TreewidthA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Microbial biogeography: putting microorganisms on the map
Use of Graph Theory to Support Map Generalization
DAG-Map: graph-based FPGA technology mapping for delay optimization
The Graph Structure of the Generalized Discrete Arnold's Cat Map
Self-organizing map for clustering in the graph domain
Interactive 3D Graph SLAM for Map Correction
The “Map” in the mental map: Experimental results in dynamic graph drawing
Radio Map Interpolation Using Graph Signal Processing
🆕 Influential since 2022
Graph attention network with Granger causality map for fault detection and root cause diagnosis
A Graph Neural Network Based Radio Map Construction Method for Urban Environment
Spatio-Temporal Context Graph Transformer Design for Map-Free Multi-Agent Trajectory Prediction
GraphMM: Graph-Based Vehicular Map Matching by Leveraging Trajectory and Road Correlations
Map-Adaptive Multimodal Trajectory Prediction Using Hierarchical Graph Neural Networks
📚 Books worth reading
Graph coloring problemsTommy R. Jensen · 1995
Graphs on surfaces and their applicationsS. K. Lando, Sergei K. Lando · 2003
Combinatorial dynamics and entropy in dimension oneLl Alsedà, Lluis Alseda · 1993
Edge-colourings of graphsStanley Fiorini · 1977
Probabilistic Methods in Discrete MathematicsValentin F. Kolchin · 1995
Analysis of class teacher timetable problemsGeorge Aron Neufeld · 1973
Map color theoremGerhard Ringel · 1974
An atlas of the smaller maps in orientable and nonorientable surfacesD. M. Jackson, David Jackson · 2000
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Bidimensionality Bidimensionality theory characterizes a broad range of graph problems (bidimensional) that admit efficient approximate, fixed-parameter or kernel solutions…
- Treewidth 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…
- Baker's technique In theoretical computer science, Baker's technique is a method for designing polynomial-time approximation schemes (PTASs) for problems on planar graphs…
- Graph minor 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…
- Dense subgraph In graph theory and computer science, a dense subgraph is a subgraph with many edges per vertex. This is formalized as follows: let G = (V, E) be an undirected…
- 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…
- Independent set (graph theory) In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a…
- Vertex cover In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph.…