Book Thickness Calculator

book embedding pages

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About Book Thickness Calculator

A book thickness calculator computing bt(G): minimum pages in book embedding (vertices on spine, edges on pages without crossing). bt=1 iff outerplanar. bt(K_n)=⌈n/2⌉. Planar graphs: bt≤4 (Yannakakis, 1989). Client-side.

Book Thickness Calculator Features

  • bt(G) pages
  • Spine ordering
  • Outerplanar bt=1
  • Planar ≤4
  • Common graphs
Book thickness bt(G): place vertices on a line (spine), assign edges to pages so no two edges on the same page cross. bt=1 iff outerplanar. bt(planar) ≤ 4 (Yannakakis). bt(K_n) = ⌈n/2⌉. Also called stack number.

How to Use

Select graph:

  • bt: Book thickness
  • Pages: Edge assignment
  • Spine: Vertex order

Planar Graphs

Every planar graph has bt ≤ 4 (Yannakakis, 1989). Some planar graphs need 4 pages. Outerplanar: bt=1 (edges form a non-crossing set). Series-parallel: bt ≤ 2. Halin graphs: bt = 2.

Applications

VLSI layout: stack layout of circuits. Fault-tolerant computing: data layout. Compiler optimization: register allocation. Computational geometry: point visibility. Book embeddings model linear data structures.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Compute bt(G).
  3. 3Find spine order.
  4. 4Assign pages.
  5. 5Verify no crossings.

Book Thickness Calculator — Frequently Asked Questions

What's a book embedding?+

Vertices on a line (spine of a book). Edges drawn as arcs on pages (half-planes). Each page: no two edges cross. Minimum pages = book thickness. Think: stack each page like a book.

How does bt relate to queue number?+

Queue number qn(G): edges in queues (FIFO) instead of stacks (LIFO). bt and qn are related but different. Planar graphs have bounded qn (Dujmović et al., 2020). bt can differ significantly from qn.

What's bt(K_n)?+

bt(K_n) = ⌈n/2⌉. Place vertices 1,...,n on spine. Page i gets edges forming a 'rainbow' pattern. Exactly ⌈n/2⌉ pages needed and sufficient. Clean combinatorial result.

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