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Minimizing the Oriented Diameter of a Planar Graph [PDF]

Electronic Notes in Discrete Mathematics, 2009
We consider the problem of minimizing the diameter of an orientation of a planar graph. A result of Chvátal and Thomassen shows that for general graphs, it is NP-complete to decide whether a graph can be oriented so that its diameter is at most two.
Steven Noble
exaly   +2 more sources

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Representations of Planar Graphs

SIAM Journal on Discrete Mathematics, 1993
Summary: This paper shows that every 3-connected planar graph \(G\) can be represented as a collection of circles, one circle representing each vertex and each face, so that, for each edge of \(G\), the four circles representing the two endpoints and the two neighboring faces meet at a point, and furthermore the vertex-circles cross the face-circles at
Graham R. Brightwell, Edward R. Scheinerman   +1 more
openaire   +1 more source

Planar Bus Graphs

Algorithmica, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Till Bruckdorfer, Stefan Felsner, Michael Kaufmann 0001   +2 more
openaire   +1 more source

On Planar Toeplitz Graphs

Graphs and Combinatorics, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Euler, Reinhardt, Zamfirescu, Tudor
openaire   +4 more sources

Partitioning Planar Graphs

SIAM Journal on Computing, 1992
The graph partitioning problem is the problem of dividing a given graph of \(n\) nodes into two sets of prescribed size while cutting a minimum number of edges. The authors show that the partitioning problem of a planar graph can be solved in polynomial time if the cutsize of the optimal partition is \(O(\log n)\) or if an embedding of the graph is ...
Thang Nguyen Bui, Andrew Peck
openaire   +3 more sources

Planarity and Hyperbolicity in Graphs

Graphs and Combinatorics, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Walter Carballosa, Ana Portilla, José M. Rodríguez 0001, José María Sigarreta   +3 more
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On the Equitable Edge-Coloring of 1-Planar Graphs and Planar Graphs

Graphs and Combinatorics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daiqiang Hu, Jian-Liang Wu 0001, Donglei Yang, Xin Zhang 0017   +3 more
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Drawing Planar Graphs Symmetrically, III: Oneconnected Planar Graphs

Algorithmica, 2005
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Seok-Hee Hong 0001, Peter Eades
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Drawing Planar Graphs Symmetrically, II: Biconnected Planar Graphs

Algorithmica, 2005
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Seok-Hee Hong 0001, Peter Eades
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