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Fitting Planar Graphs on Planar Maps [PDF]

Journal of Graph Algorithms and Applications, 2015
Graph and cartographic visualization have the common objective to provide intuitive understanding of some underlying data. We consider a problem that combines aspects of both by studying the problem of fitting planar graphs on planar maps.
Md. Jawaherul Alam, Michael Kaufmann, Stephen Kobourov, Tamara Mchedlidze   +3 more
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Intuitionistic Fuzzy Planar Graphs

Discrete Dynamics in Nature and Society, 2014
Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty
Noura Alshehri, Muhammad Akram
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Cubic planar graphs that cannot be drawn on few lines

Journal of Computational Geometry, 2021
For every integer $\ell$, we construct a cubic 3-vertex-connected planar bipartite graph $G$ with $O(\ell^3)$ vertices such that there is no planar straight-line drawing of $G$ whose vertices all lie on $\ell$ lines.
David Eppstein
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Rook-drawings of Plane Graphs

Journal of Graph Algorithms and Applications, 2017
We introduce a new type of graph drawing called "rook-drawing". A rook-drawing of a graph $G$ is obtained by placing the $n$ nodes of $G$ on the intersections of a regular grid, such that each row and column of the grid supports exactly one node.
David Auber, Nicolas Bonichon, Paul Dorbec, Claire Pennarun   +3 more
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A Note on Universal Point Sets for Planar Graphs

Journal of Graph Algorithms and Applications, 2020
We investigate which planar point sets allow simultaneous straight-line embeddings of all planar graphs on a fixed number of vertices. We first show that at least $(1.293-o(1))n$ points are required to find a straight-line drawing of each $n$-vertex ...
Manfred Scheucher, Hendrik Schrezenmaier, Raphael Steiner   +2 more
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Total Coloring of Dumbbell Maximal Planar Graphs

Mathematics, 2022
The Total Coloring Conjecture (TCC) states that every simple graph G is totally (Δ+2)-colorable, where Δ denotes the maximum degree of G. In this paper, we prove that TCC holds for dumbbell maximal planar graphs.
Yangyang Zhou, Dongyang Zhao, Mingyuan Ma, Jin Xu   +3 more
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Relaxed DP-Coloring and another Generalization of DP-Coloring on Planar Graphs without 4-Cycles and 7-Cycles

Discussiones Mathematicae Graph Theory, 2023
DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute, Nakprasit Keaitsuda Maneeruk, Nakprasit Kittikorn, Sittitrai Pongpat   +3 more
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Note on robust coloring of planar graphs [PDF]

Opuscula Mathematica
We consider the robust chromatic number \(\chi_1(G)\) of planar graphs \(G\) and show that there exists an infinite family of planar graphs \(G\) with \(\chi_1(G) = 3\), thus solving a recent problem of Bacsó et al.
František Kardoš, Borut Lužar, Roman Soták   +2 more
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On Aligned Bar 1-Visibility Graphs

Journal of Graph Algorithms and Applications, 2017
A graph is called a bar 1-visibility graph if its vertices can be represented as horizontal segments, called bars, and each edge corresponds to a vertical line of sight which can traverse another bar.
Franz Brandenburg, Alexander Esch, Daniel Neuwirth   +2 more
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Degeneracies of Triangulated Graphs

Theory and Applications of Graphs
A graph $G$ is $k$-degenerate if each subgraph has minimum degree at most $k$. The degeneracy\textbf{ }$D\left(G\right)$ is the smallest $k$ such that $G$ is $k$-degenerate.
Allan Bickle
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