Results 291 to 300 of about 38,199 (317)

Clique graphs of planar graphs.

Ars Comb., 2004
The 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
openaire   +1 more source

On Partitioning Planar Graphs

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.
openaire   +2 more sources

Planarity for clustered graphs

1995
In 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, Robert F. Cohen, Peter Eades   +2 more
openaire   +1 more source

Formalization of planar graphs

1995
Among 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, Shin-ya Nishizaki, Masami Hagiya, Yozo Toda   +3 more
openaire   +1 more source

Interval valued m-polar fuzzy planar graph and its application

Artificial Intelligence Review, 2020
Tanmoy Mahapatra, Sankar Sahoo, Ganesh Ghorai   +2 more
exaly  

The maximum number of paths of length four in a planar graph

Discrete Mathematics, 2021
Debarun Ghosh, Ervin Gyori, Ryan R Martin   +2 more
exaly  

The Alon-Tarsi number of a planar graph minus a matching

Journal of Combinatorial Theory Series B, 2020
Jarosław Grytczuk, Xuding Zhu
exaly  

Every planar graph with girth at least 5 is (1,9)-colorable

Discrete Mathematics, 2022
Xiangwen Li
exaly  

Coloring the square of a planar graph

Journal of Graph Theory, 2003
Jan Van den Heuvel
exaly  

A bound on the chromatic number of the square of a planar graph

Journal of Combinatorial Theory Series B, 2005
Mohammad R Salavatipour
exaly