Results 11 to 20 of about 179,348 (60)
Planar Transitive Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that
openaire +3 more sources
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
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Contact Representations of Graphs in 3D
, 2015 We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there
A Bezdek +17 more
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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
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Computing Planarity in Computable Planar Graphs
Graphs and Combinatorics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oscar Levin, Taylor McMillan
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Recognizing and Drawing IC-planar Graphs
, 2015 IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs.
C Auer +27 more
core +1 more source
Diameter and Treewidth in Minor-Closed Graph Families
, 1999 It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families.
Eppstein, David
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The Weisfeiler-Leman Dimension of Planar Graphs is at most 3
, 2017 We prove that the Weisfeiler-Leman (WL) dimension of the class of all finite planar graphs is at most 3. In particular, every finite planar graph is definable in first-order logic with counting using at most 4 variables.
Kiefer, Sandra +2 more
core +1 more source
Near-colorings: non-colorable graphs and NP-completeness [PDF]
, 2013 A graph G is (d_1,..,d_l)-colorable if the vertex set of G can be partitioned into subsets V_1,..,V_l such that the graph G[V_i] induced by the vertices of V_i has maximum degree at most d_i for all 1
Montassier, Mickael, Ochem, Pascal
core
A Planarity Test via Construction Sequences
, 2012 Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests.
A.K. Kelmans +20 more
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