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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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Clique graphs of planar graphs.
Ars Comb., 2004The main result of this paper is a characterization of those \(K_3\)-free or \(K_4\)-free graphs which occur as the clique graphs of planar graphs. Several examples are given of planar graphs which do not occur as clique graphs of planar graphs.
Liliana Alcón, Marisa Gutierrez
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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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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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Formalization of planar graphs
1995Among many fields of mathematics and computer science, discrete mathematics is one of the most difficult fields to formalize because we prove theorems using intuitive inferences that have not been rigorously formalized yet. This paper focuses on graph theory from discrete mathematics and formalizes planar graphs.
Mitsuharu Yamamoto +3 more
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Interval Valued m-Polar Fuzzy Planar Graph and Its Application
Artificial Intelligence Review, 2021Ganesh Ghorai +2 more
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Generalized Neutrosophic Planar Graphs and Its Application
Journal of Applied Mathematics and Computing, 2021Sovan Samanta +2 more
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Planar Graphs Have Bounded Queue-Number
Journal of the ACM, 2020Vida Dujmović, David Wood, Piotr Micek
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Adjacency Labelling for Planar Graphs (and Beyond)
Journal of the ACM, 2021Louis Espéret +2 more
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IC-Planar Graphs Are 6-Choosable
SIAM Journal on Discrete Mathematics, 2021Weifan Wang, Yiqiao Wang, Ko-Wei Lih
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