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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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Journal of Graph Theory, 1997
Let \(G\) be a 2-connected plane graph and let \(X_G\) be the circuit bounding the infinite face. This paper generalizes the following result by \textit{C. Thomassen} [J. Graph Theory 7, 169-176 (1983; Zbl 0515.05040)], which in turn was an improvement of an earlier theorem by \textit{W. T. Tutte} [Trans. Am. Math. Soc. 82, 99-116 (1956; Zbl 0070.18403)
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Let \(G\) be a 2-connected plane graph and let \(X_G\) be the circuit bounding the infinite face. This paper generalizes the following result by \textit{C. Thomassen} [J. Graph Theory 7, 169-176 (1983; Zbl 0515.05040)], which in turn was an improvement of an earlier theorem by \textit{W. T. Tutte} [Trans. Am. Math. Soc. 82, 99-116 (1956; Zbl 0070.18403)
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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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Australas. J Comb., 1998
It is known that for an arbitrary graph on \(n\) vertices, the minimum time required to broadcast is \(\lceil \log_2n\rceil\), and for any \(n\), there exist graphs on \(n\) vertices with broadcast time equal to \(\lceil\log_2 n\rceil\). When restricted to planar graphs, this is generally not the case. In this paper, the planar broadcast time for \(n\),
Pavol Hell, Karen Seyffarth
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It is known that for an arbitrary graph on \(n\) vertices, the minimum time required to broadcast is \(\lceil \log_2n\rceil\), and for any \(n\), there exist graphs on \(n\) vertices with broadcast time equal to \(\lceil\log_2 n\rceil\). When restricted to planar graphs, this is generally not the case. In this paper, the planar broadcast time for \(n\),
Pavol Hell, Karen Seyffarth
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Morphing Planar Graph Drawings Efficiently
International Symposium Graph Drawing and Network Visualization, 2013Patrizio Angelini +3 more
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Density of straight-line 1-planar graph drawings
Information Processing Letters, 2013W. Didimo
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An improved Cuckoo Search Algorithm for Solving Planar Graph Coloring Problem
, 2013Yongquan Zhou +4 more
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The maximum number of paths of length four in a planar graph
Discrete Mathematics, 2021Ervin Gyori +2 more
exaly
How to draw a planar graph on a grid
Comb., 1990Hubert de Fraysseix, J. Pach, R. Pollack
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