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Explore the main themes, entities and connections around Eulerian path. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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Counting Eulerian circuits
17 related topics
Applications
6 related topics
Definition
8 related topics
Constructing Eulerian trails and circuits
6 related topics
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Graph theory
- Trail Trail (graph theory)
- Graph Graph (discrete mathematics)
- Edge Edge (graph theory)
- Vertex Vertex (graph theory)
- Leonhard Euler
- Seven Bridges of Königsberg
- Path Path (graph theory)
- Cycle Cycle (graph theory)
- Proved Mathematical proof
- Odd Parity (mathematics)
- Degree Degree (graph theory)
- Connected graphs Connectivity (graph theory)
- Carl Hierholzer
- If and only if
Definition
- Undirected graph
- Connected graphs Connected graph
- Outdegree Directed graph
- Directed path Directed path (graph theory)
- Directed cycle
- Multigraphs Multigraph
- Strong orientation
- Strongly connected
Properties
- Connected component Connected component (graph theory)
- In-degree In degree (graph theory)
- Out-degree Out degree (graph theory)
- Strongly connected component
Constructing Eulerian trails and circuits
- Bridge-finding algorithm Bridge (graph theory)
- Tarjan Robert Tarjan
- Thorup (2000) Eulerian path
- Doubly linked list
- Linear time
- Deque Double-ended queue
Counting Eulerian circuits
- BEST theorem
- De Bruijn N. G. de Bruijn
- Van Aardenne-Ehrenfest Tatyana Pavlovna Ehrenfest
- Smith Cedric Smith (statistician)
- Tutte W. T. Tutte
- Arborescences Arborescence (graph theory)
- Determinant
- Matrix tree theorem
- Bijective Bijective proof
- De Bruijn sequences De Bruijn sequence
- #P-complete Sharp-P-complete
- Markov chain Monte Carlo
- Anton Kotzig
- Asymptotic formula Asymptotic analysis
- Complete graphs Complete graph
- McKay Brendan McKay (mathematician)
- Complete bipartite graphs Complete bipartite graph
Applications
- Bioinformatics
- DNA sequence
- CMOS
- Logic gate
- Trees Tree (graph theory)
- De Bruijn graphs De Bruijn graph
In infinite graphs
- Infinite graph
- Cayley graph
- Countable sets Countable set
Mixed Eulerian graphs
- Mixed graphs Mixed graph
- Ford L. R. Ford Jr.
- Fulkerson D. R. Fulkerson
Eulerian cycles and bridges
Bibliography
- Erdős, P. Paul Erdős
- Grünwald, T. Tibor Gallai
- Weiszfeld, Endre Andrew Vázsonyi
- Doi Doi (identifier)
- Mathematische Annalen
- S2CID S2CID (identifier)
- N. G. de Bruijn Nicolaas Govert de Bruijn
- Simon Stevin Simon Stevin (journal)
- Thorup, Mikkel Mikkel Thorup
- Proc. 32nd ACM Symposium on Theory of Computing Symposium on Theory of Computing
- American Mathematical Monthly
Advanced semantic analysis
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Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Eulerian path
Nodes85
Edges84
Triples8
Avg. degree1.98
Density0.023529
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
Eulerian path
Top relations
see also · 4
Eulerian path → Euler, Eulerian, Route, Veblen's
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
Important terminology
eulerian graph degree connected vertices vertex graphs even every trail undirected cycle edges algorithm euler edge two odd directed circuits
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| a doubly linked list to maintain the set of unused edges incident to each vertex | instance of | repeating the previous step will exhaust all edges of the graph.By using a data structure | 0.80 | text |
| to maintain the list of vertices on the current tour that have unused edges | instance of | repeating the previous step will exhaust all edges of the graph.By using a data structure | 0.80 | text |
| and to maintain the tour itself | instance of | repeating the previous step will exhaust all edges of the graph.By using a data structure | 0.80 | text |
| the individual operations of the algorithm | instance of | repeating the previous step will exhaust all edges of the graph.By using a data structure | 0.80 | text |
| Eulerian path | see also | Eulerian | 0.60 | section |
| Eulerian path | see also | Euler | 0.60 | section |
| Eulerian path | see also | Route | 0.60 | section |
| Eulerian path | see also | Veblen's | 0.60 | section |
No triples extracted yet.
Related concept clusters Concept neighborhoods
Clusters of nearby vocabulary surrounding the topic. Scan them for adjacent concepts and language you may have missed.These clusters group vocabulary that occurs around closely connected concepts in the source material.
Connections between topic areas Semantic bridges
Bridge nodes connect otherwise separate parts of the map. Expand a row to inspect the topic groups on each side.Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.
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