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Everything about Critical graph
Undirected graph
In graph theory, a critical graph is an undirected graph all of whose proper subgraphs have smaller chromatic number. In such a graph, every vertex or edge is a critical element, in the sense that its deletion would decrease the number of colors needed in a graph coloring of the given graph. Each time a single edge or vertex is removed from a critical graph, the decrease in the number of colors needed to color that graph cannot be by more than one. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Critical graphA 5-minute orientation
- Skim a recent paper: A critical review on graphitic carbon nitride (g-C3N4)-based materials: Preparation, modification and environmental applicationInfluential work since 2022
- Pick up a classic book: Graphs, Networks and DesignThe most-reprinted book on the subject
- Read the landmark paper: Feynman-Graph Expansion for Critical ExponentsCited 577 times
- Go sideways: Hadwiger conjecture (graph theory)A closely related topic
- Go sideways: HajĂłs constructionA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Feynman-Graph Expansion for Critical Exponents
Tree graph inequalities and critical behavior in percolation models
Chip-Firing and the Critical Group of a Graph
Latent Graph Representations for Critical View of Safety Assessment
Identifying Critical Elements in Sewer Networks Using Graph-Theory
Skeleton Graph Expansion for Critical Exponents
Cycles in a random graph near the critical point
The critical complexity of graph properties
🆕 Influential since 2022
A critical review on graphitic carbon nitride (g-C3N4)-based materials: Preparation, modification and environmental application
Edge-based graph neural network for ranking critical road segments in a network
The stable graph: The metric space scaling limit of a critical random graph with i.i.d. power-law degrees
A graph-empowered agent-based simulation: Impacts of coordination schemes on critical infrastructures resilience
Aging-Aware Critical Path Selection via Graph Attention Networks
đź“š Books worth reading
Graphs, Networks and DesignMT365 Course Team · 1995
Probability and statistical physics in two and more dimensionsClay Mathematics Institute. Summer School · 2012
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
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