Results 61 to 70 of about 1,442,532 (348)
On random planar graphs, the number of planar graphs and their triangulations
Journal of Combinatorial Theory, Series B, 2003 AbstractLet Pn be the set of labelled planar graphs with n vertices. Denise, Vasconcellos and Welsh proved that |Pn|⩽n!(75.8)n+o(n) and Bender, Gao and Wormald proved that |Pn|⩾n!(26.1)n+o(n). Gerke and McDiarmid proved that almost all graphs in Pn have at least 13/7n edges.
Deryk Osthus +2 more
openaire +1 more source
Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
, 2018 We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively.
C Bachmaier +13 more
core +1 more source
Morphing Planar Graph Drawings Optimally [PDF]
, 2014 We provide an algorithm for computing a planar morph between any two planar straight-line drawings of any $n$-vertex plane graph in $O(n)$ morphing steps, thus improving upon the previously best known $O(n^2)$ upper bound.
C. Erten +10 more
core +1 more source
Inapproximability of the Tutte polynomial of a planar graph [PDF]
Computational Complexity, 2009 The Tutte polynomial of a graph G is a two-variable polynomial T(G; x, y) that encodes many interesting properties of the graph. We study the complexity of the following problem, for rationals x and y: given as input a planar graph G, determine T(G; x, y)
L. A. Goldberg, M. Jerrum
semanticscholar +1 more source
Obstacle Numbers of Planar Graphs
, 2017 Given finitely many connected polygonal obstacles $O_1,\dots,O_k$ in the plane and a set $P$ of points in general position and not in any obstacle, the {\em visibility graph} of $P$ with obstacles $O_1,\dots,O_k$ is the (geometric) graph with vertex set $
B Mohar +9 more
core +1 more source
On Computation of Degree-Based Entropy of Planar Octahedron Networks
Journal of Function Spaces, 2022 Chemical graph theory is the combination of mathematical graph theory and chemistry. To analyze the biocompatibility of the compounds, topological indices are used in the research of QSAR/QSPR studies.
Tian-Le Sun +5 more
doaj +1 more source
Monotone Grid Drawings of Planar Graphs
, 2013 A monotone drawing of a planar graph $G$ is a planar straight-line drawing of $G$ where a monotone path exists between every pair of vertices of $G$ in some direction.
E.M. Arkin +6 more
core +1 more source
Treewidth 2 in the Planar Graph Product Structure Theorem [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe prove that every planar graph is contained in $H_1\boxtimes H_2\boxtimes K_2$ for some graphs $H_1$ and $H_2$ both with treewidth 2. This resolves a question of Liu, Norin and Wood [arXiv:2410.20333]. We also show this result is best possible: for any
Marc Distel +4 more
doaj +1 more source
Every Planar Map Is Four Colorable
Mathematical Solitaires & Games, 2019 As has become standard, the four color map problem will be considered in the dual sense as the problem of whether the vertices of every planar graph (without loops) can be colored with at most four colors in such a way that no pair of vertices which lie ...
K. Appel, W. Haken
semanticscholar +1 more source
, 2017 We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with nice convex drawings: outer $k$-planar graphs, where each edge is crossed by at
AWM Dress +23 more
core +1 more source