Ehrenfeucht-Fraisse Game for Finite Graphs

This browser puzzle turns an Ehrenfeucht–Fraïssé game into a hands-on comparison of two finite graphs. Pick vertices as Spoiler while a Duplicator opponent tries to preserve the illusion that both networks have the same local structure.

What is Ehrenfeucht-Fraisse Game for Finite Graphs?

Two networks sit side by side, full of shaped vertices and edges. Your job is to choose a vertex in either graph; the Duplicator answers with a same-colored match in the other. A mismatch in shape or adjacency breaks the correspondence, so the real puzzle is spotting a structural difference that the opponent cannot keep disguising. The page supplies the rules, a hint key, and a mode for dragging vertices, turning a fairly lofty idea from first-order logic into something you can prod with a cursor.

What you can do there

• Choose vertices in one of two graphs
• Test whether matched vertices preserve shapes and edges
• Use hints or rearrange the graph layout

Why we picked it

There are plenty of pages that explain formal logic and far fewer that let you poke it until it loses. This small implementation makes the Spoiler-versus-Duplicator metaphor concrete without sanding off the mathematical point.

How to get the most from it

Read the short rules before clicking. Choose an unused vertex in either graph and watch where Duplicator answers; then look for an edge or shape relationship that cannot be mirrored. Press H for a hint, M to switch between moves and layout dragging, or N for a fresh game.

Good to know

This is an English-language HTML5 puzzle with mouse selection and documented H, M, and N shortcuts. The page warns that its Duplicator AI simply forfeits when no suitable response exists. Runtime behavior, difficulty, touch support, accessibility, audio, and the full graph inventory were not independently tested.

Who made it, and when?

trkern is the credited creator or organization.