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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 ...
Thang Nguyen Bui, Andrew Peck
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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 ...
Thang Nguyen Bui, Andrew Peck
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Planarity and Hyperbolicity in Graphs
Graphs and Combinatorics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Walter Carballosa +3 more
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Every planar graph has an acyclic 7-coloring
Israel Journal of Mathematics, 1977Michael O Albertson
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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.
Daiqiang Hu +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.
Seok-Hee Hong 0001, Peter Eades
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On the Number of Spanning Trees a Planar Graph Can Have
Embedded Systems and Applications, 2009We prove that any planar graph on n vertices has less than O(5.2852n) spanning trees. Under the restriction that the planar graph is 3-connected and contains no triangle and no quadrilateral the number of its spanning trees is less than O(2.7156n).
K. Buchin, A. Schulz
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Drawing Planar Graphs Symmetrically, II: Biconnected Planar Graphs
Algorithmica, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seok-Hee Hong 0001, Peter Eades
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A GRASP for graph planarization
Networks, 1997Summary: A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. We describe a GRASP for the graph planarization problem, extending the heuristic of \textit{O. Goldschmidt} and \textit{A. Takvorian} [Networks 24, No. 2, 69-73 (1994; Zbl 0789.90083)].
Mauricio G. C. Resende, Celso C. Ribeiro
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Generalizations of planar graphs
Networks, 1982AbstractTwo new generalizations of planar graphs, called quasiplanar and pseudoplanar graphs, are introduced and discussed. It is shown that planar graphs are quasiplanar and these in turn are pseudoplanar. Conversely, a pseudoplanar graph that contains with each arc its reverse arc is quasiplanar.
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Planarity for clustered graphs
1995In this paper, we introduce a new graph model known as clustered graphs, i.e. graphs with recursive clustering structures. This graph model has many applications in informational and mathematical sciences. In particular, we study C-planarity of clustered graphs.
Qing-Wen Feng +2 more
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