1,856 research outputs found
Crossing Minimization for 1-page and 2-page Drawings of Graphs with Bounded Treewidth
We investigate crossing minimization for 1-page and 2-page book drawings. We
show that computing the 1-page crossing number is fixed-parameter tractable
with respect to the number of crossings, that testing 2-page planarity is
fixed-parameter tractable with respect to treewidth, and that computing the
2-page crossing number is fixed-parameter tractable with respect to the sum of
the number of crossings and the treewidth of the input graph. We prove these
results via Courcelle's theorem on the fixed-parameter tractability of
properties expressible in monadic second order logic for graphs of bounded
treewidth.Comment: Graph Drawing 201
Two-Page Book Embeddings of 4-Planar Graphs
Back in the Eighties, Heath showed that every 3-planar graph is
subhamiltonian and asked whether this result can be extended to a class of
graphs of degree greater than three. In this paper we affirmatively answer this
question for the class of 4-planar graphs. Our contribution consists of two
algorithms: The first one is limited to triconnected graphs, but runs in linear
time and uses existing methods for computing hamiltonian cycles in planar
graphs. The second one, which solves the general case of the problem, is a
quadratic-time algorithm based on the book-embedding viewpoint of the problem.Comment: 21 pages, 16 Figures. A shorter version is to appear at STACS 201
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
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