2:I[5751,[],""] 4:I[8003,["138","static/chunks/138-338b445c4cbceabf.js","3","static/chunks/3-b4862a6e1de95ec0.js","628","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/%5Bid%5D/page-257c971832fd49dc.js"],"default"] 6:I[9275,[],""] a:I[1343,[],""] b:I[101,["138","static/chunks/138-338b445c4cbceabf.js","987","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/layout-3942c697a7972a68.js"],"default"] c:I[6324,["138","static/chunks/138-338b445c4cbceabf.js","987","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/layout-3942c697a7972a68.js"],"default"] 13:I[4080,["185","static/chunks/app/layout-f07fbac6855a712f.js"],""] 14:I[231,["138","static/chunks/138-338b445c4cbceabf.js","986","static/chunks/986-a23d2b0476d0b49a.js","368","static/chunks/app/papers/%5BpaperId%5D/page-879e8aaf99bd7bd0.js"],""] 16:I[6130,[],""] 5:T4db,

Answer: ["A","B","D"]

Key insight
An Eulerian path (drawing without lifting the pen) exists if and only if the graph has exactly 0 or 2 vertices of odd degree. Count odd-degree vertices in each figure.

Step by step
Step 1: Recall the Eulerian path rule: a connected graph can be drawn without lifting the pen if it has 0 or 2 vertices with an odd number of edges meeting at them.
Step 2: Figure A — count vertices and their degrees. Result: 0 or 2 odd-degree vertices. ✓
Step 3: Figure B — same analysis. Result: 0 or 2 odd-degree vertices. ✓
Step 4: Figure C — count odd-degree vertices. Result: more than 2 odd-degree vertices. ✗
Step 5: Figure D — count odd-degree vertices. Result: 0 or 2 odd-degree vertices. ✓
Therefore the answer is A, B, and D.

Why wrong options are wrong
Option C: The figure has more than 2 vertices of odd degree, making an Eulerian path impossible.

Remember for exam
Euler's rule is the fastest check: count edges at each vertex; if more than 2 vertices have an odd count, you cannot draw it without

Which of the given figures can be drawn without lifting the pen? The lines can cross each other but cannot overlap on top of one another.