What’s on the Euler & Hamiltonian Paths poster
Euler path against Hamiltonian path, side by side.
- Euler path: Uses every edge exactly once
- Euler path: Exists iff 0 or 2 vertices have odd degree
- Euler path: A circuit needs every degree even
- Euler path: The graph must be connected
- Euler path: Decidable in linear time
- Euler path: Fleury's or Hierholzer's algorithm finds one
- Hamiltonian path: Visits every vertex exactly once
- Hamiltonian path: No simple criterion is known
- Hamiltonian path: Deciding it is NP-complete
- Hamiltonian path: Dirac: every degree ≥ n/2 suffices
- Hamiltonian path: Ore's condition is also sufficient
- Hamiltonian path: Both are sufficient, never necessary
- Edges are easy and vertices are hard. Euler has a clean degree test; Hamilton has not…
Dirac's theorem needs n ≥ 3 and every degree at least n/2. It guarantees a Hamiltonian cycle exists but does not construct one.
Questions about the Euler & Hamiltonian Paths poster
- What’s on the Euler & Hamiltonian Paths poster?
- Euler path against Hamiltonian path, side by side. Euler path: Uses every edge exactly once; Euler path: Exists iff 0 or 2 vertices have odd degree; Euler path: A circuit needs every degree even; Euler path: The graph must be connected; Euler path: Decidable in linear time; Euler path: Fleury's or Hierholzer's algorithm finds one; Hamiltonian path: Visits every vertex exactly once; Hamiltonian path: No simple criterion is known; Hamiltonian path: Deciding it is NP-complete; Hamiltonian path: Dirac: every degree ≥ n/2 suffices; Hamiltonian path: Ore's condition is also sufficient; Hamiltonian path: Both are sufficient, never necessary; Edges are easy and vertices are hard. Euler has a clean degree test; Hamilton has not…. Dirac's theorem needs n ≥ 3 and every degree at least n/2. It guarantees a Hamiltonian cycle exists but does not construct one.
- Who is the Euler & Hamiltonian Paths poster for?
- Euler & Hamiltonian Paths belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning discrete mathematics can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Euler & Hamiltonian Paths poster?
- When asked whether a route can use every edge, or visit every vertex, exactly once. A wall chart earns its place by being glanceable from where the work is happening, so Euler & Hamiltonian Paths belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Euler & Hamiltonian Paths?
- The Binomial Theorem, Counting Principles and Graph Vocabulary sit alongside Euler & Hamiltonian Paths in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Binomial TheoremCounting PrinciplesGraph Vocabulary
- Is the Euler & Hamiltonian Paths poster free to download and print?
- Yes. Euler & Hamiltonian Paths downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Euler & Hamiltonian Paths poster print at?
- Euler & Hamiltonian Paths is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Euler & Hamiltonian Paths loses nothing.Printing guide
Related posters
Charts that sit alongside Euler & Hamiltonian Paths on the same wall.
Browse every Mathematics poster, or start from the full catalogue.