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Representations of Planar Graphs
SIAM Journal on Discrete Mathematics, 1993Summary: 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
Brightwell, Graham R. +1 more
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Algorithmica, 2017
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Bruckdorfer, Till +2 more
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Bruckdorfer, Till +2 more
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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 ...
Bui, Thang Nguyen, Peck, Andrew
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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 ...
Bui, Thang Nguyen, Peck, Andrew
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Planarity and Hyperbolicity in Graphs
Graphs and Combinatorics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carballosa, Walter +3 more
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Graphs and Combinatorics, 2012
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Euler, Reinhardt, Zamfirescu, Tudor
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Euler, Reinhardt, Zamfirescu, Tudor
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On the Equitable Edge-Coloring of 1-Planar Graphs and Planar Graphs
Graphs and Combinatorics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hu, Dai-Qiang +3 more
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Drawing Planar Graphs Symmetrically, III: Oneconnected Planar Graphs
Algorithmica, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong, Seok-Hee, Eades, Peter
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Canadian Mathematical Bulletin, 1968
In 1879 Kempe [5] presented what has become the most famous of all incorrect proofs of the Four Colour Conjecture, but even though his proof was erroneous his method has become quite useful. In 1890 Heawood [4] was able to modify Kempe's method to establish the Five Colour Theorem for planar graphs.
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In 1879 Kempe [5] presented what has become the most famous of all incorrect proofs of the Four Colour Conjecture, but even though his proof was erroneous his method has become quite useful. In 1890 Heawood [4] was able to modify Kempe's method to establish the Five Colour Theorem for planar graphs.
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Drawing Planar Graphs Symmetrically, II: Biconnected Planar Graphs
Algorithmica, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong, Seok-Hee, Eades, Peter
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