Threshold Graph Checker

isolated + dominating build

CheckersFreeNo Signup
4.6(427 reviews)
All Tools

Loading tool...

About Threshold Graph Checker

A threshold graph checker testing if G can be built by iteratively adding isolated vertices (degree 0) or dominating vertices (adjacent to all existing). Threshold ⊂ split ⊂ chordal. Degree sequence uniquely determines threshold graph. O(n+m). Client-side.

Threshold Graph Checker Features

  • Threshold test
  • Build sequence
  • Degree unique
  • Split subclass
  • O(n+m)
Threshold graph: built iteratively from empty graph by adding isolated vertex (0 edges) or dominating vertex (edges to all existing). Creation sequence: string of 0s and 1s. Threshold ⊂ split ⊂ chordal ⊂ perfect. Uniquely determined by degree sequence.

How to Use

Select graph:

  • Test: Threshold?
  • Sequence: 0/1 build
  • Degree: Unique check

Creation Sequence

Binary string b₁...bₙ: bᵢ=0 (add isolated), bᵢ=1 (add dominating). Example: K_3 = 0,1,1 (start isolated, then two dominating). Every threshold graph has a unique creation sequence (up to initial vertex).

Characterization

Equivalent: no induced 2K₂, C₄, or P₄. Also: degree sequence uniquely determines the graph (no two non-isomorphic threshold graphs have the same degree sequence). Extremely structured class.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Check threshold.
  3. 3Find sequence.
  4. 4Verify degrees.
  5. 5Apply properties.

Threshold Graph Checker — Frequently Asked Questions

How are threshold graphs related to split?+

Every threshold graph is split (K∪I partition exists). Not every split graph is threshold: split allows edges between I vertices and K vertices freely; threshold restricts to creation sequence. Threshold ⊊ split.

What's special about degree sequences?+

Threshold graphs are uniquely determined by their degree sequence! No other graph class has this property so broadly. Given a degree sequence, you can check if it's threshold and reconstruct the graph in O(n) time.

What's the forbidden subgraph characterization?+

G is threshold iff no induced 2K₂ (two disjoint edges), C₄ (4-cycle), or P₄ (4-path). Very restrictive: forbids all of these simultaneously. Equivalently: {2K₂, C₄, P₄}-free.

More Checkers Tools

Explore all 223 other checkers tools available on Generatr

Academic Readability Graderads.txt ValidatorAI Content DetectorAlexander McQueen Serial Number CheckerAnagram CheckerAnalog Gem Tester SimulatorAnsible LinterArc-Transitive Graph CheckerAudemars Piguet Serial Number CheckerAuto Parts Compatibility CheckerBike Serial Number CheckerBlocked Checker TwitterBluesky Block CheckerBottega Veneta Serial Number CheckerBrawl Stars Mastery CheckerBulk SERP CheckerBulova Serial Number CheckerCanned Phrase & Cliche CheckerCar Stereo Compatibility CheckerCartier Love Bracelet Serial Number CheckerCartier Serial Number CheckerCeline Serial Number CheckerCetaphil Lot Number CheckerCGC Certification LookupCharacter Frequency CounterChordal Graph CheckerCircleboom Shadowban CheckerClash Royale Deck CheckerClash Royale Synergy CheckerCograph Recognition Checker
View all 223 checkers tools
Share this tool: