Results 31 to 40 of about 1,442,532 (348)
How to Morph Planar Graph Drawings [PDF]
SIAM journal on computing (Print), 2016 Given an $n$-vertex graph and two straight-line planar drawings of the graph that have the same faces and the same outer face, we show that there is a morph (i.e., a continuous transformation) between the two drawings that preserves straight-line ...
Soroush Alamdari +12 more
semanticscholar +1 more source
Connectivity of Planar Graphs [PDF]
Journal of Graph Algorithms and Applications, 2001 We give here three simple linear time algorithms on planar graphs: a 4-connexity test for maximal planar graphs, an algorithm enumerating the triangles and a 3-connexity test. Although all these problems got already linear-time solutions, the presented algorithms are both simple and efficient. They are based on some new theoretical results.
de Fraysseix, Hubert +1 more
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The number of planar graphs and properties of random planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We show an asymptotic estimate for the number of labelled planar graphs on $n$ vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in random planar graphs.
Marc Noy, Omer Giménez
openaire +5 more sources
An improved upper bound for the dynamic list coloring of 1-planar graphs
AIMS Mathematics, 2022 A graph is 1-planar if it can be drawn in the plane such that each of its edges is crossed at most once. A dynamic coloring of a graph G is a proper vertex coloring such that for each vertex of degree at least 2, its neighbors receive at least two ...
Xiaoxue Hu, Jiangxu Kong
doaj +1 more source
A note on nearly Platonic graphs with connectivity one
Electronic Journal of Graph Theory and Applications, 2021 A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek,
Dalibor Froncek +3 more
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SOME PROPERTIES ON COPRIME GRAPH OF GENERALIZED QUATERNION GROUPS
Barekeng, 2023 A coprime graph is a representation of finite groups on graphs by defining the vertex graph as an element in a group and two vertices adjacent to each other's if and only if the order of the two elements is coprime.
Arif Munandar
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An annotated bibliography on 1-planarity [PDF]
, 2017 The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge.
Kobourov, Stephen G. +2 more
core +1 more source
Computational Study on a PTAS for Planar Dominating Set Problem
Algorithms, 2013 The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time ...
Qian-Ping Gu, Marjan Marzban
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On certain prime cordial families of graphs
Journal of Taibah University for Science, 2020 Graph labelling is an important tool in modelling real life problems. In the present paper, different graph families are studied for prime cordial labelling.
Nazeran Idrees +3 more
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Sufficient Conditions of 6-Cycles Make Planar Graphs DP-4-Colorable
Mathematics, 2022 In simple graphs, DP-coloring is a generalization of list coloring and thus many results of DP-coloring generalize those of list coloring. Xu and Wu proved that every planar graph without 5-cycles adjacent simultaneously to 3-cycles and 4-cycles is 4 ...
Kittikorn Nakprasit +2 more
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