Two-Page Book Embeddings of 4-Planar Graphs

Book embeddings of Reeb graphs

Let X be a simplicial complex with a piecewise linear function f : X → R. The Reeb graph Reeb(f,X) is the quotient of X, where we collapse each connected component of f−1(t) to a single point. Let the nodes of Reeb(f,X) be all homologically critical points where any homology of the corresponding component of the level set f−1(t) changes. Then we can label every arc of Reeb(f,X) with the Betti n...

Simpler Testing for Two-page Book Embedding of Partitioned Graphs

A 2-page book embedding of a graph is to place the vertices linearly on a spine (a line segment) and the edges on the two pages (two half planes sharing the spine) so that each edge is embedded in one of the pages without edge crossings. Testing whether a given graph admits a 2-page book embedding is known to be NP-complete. In this paper, we study the problem of testing whether a given graph a...

Chordal embeddings of planar graphs

Robertson and Seymour conjectured that the treewidth of a planar graph and the treewidth of its geometric dual differ by at most one. Lapoire solved the conjecture in the affirmative, using algebraic techniques. We give here a much shorter proof of this result.

Geodesic Embeddings and Planar Graphs

Geodesi Embeddings and Planar Graphs