Results 1 to 10 of about 892,665 (298)
Drawing Partially Embedded and Simultaneously Planar Graphs
Journal of Graph Algorithms and Applications, 2015 We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem-to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph-and the simultaneous ...
Timothy Chan +5 more
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k-L(2, 1)-labelling for planar graphs is NP-complete for k>=4 [PDF]
, 2009 A mapping from the vertex set of a graph G=(V,E) into an interval of integers {0,...,k} is an L(2,1)-labelling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common ...
Noble, Steven +8 more
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The structure and the list 3-dynamic coloring of outer-1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge.
Yan Li, Xin Zhang
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Improved product structure for graphs on surfaces [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve
Marc Distel +3 more
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The nonsolvability by radicals of generic 3-connected planar Laman graphs. [PDF]
, 2007 We show that planar embeddable -connected Laman graphs are generically non-soluble. A Laman graph represents a configuration of points on the Euclidean plane with just enough distance specifications between them to ensure rigidity.
Power, Stephen C., Owen, J. C.
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Planar Projections of Graphs [PDF]
Discrete Applied Mathematics, 2020 We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on $n$ vertices has a representation in $\lceil \sqrt{n/2}+1 \rceil$ planes.
N. R. Aravind, Udit Maniyar
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Good triangulations yield good tours [PDF]
, 2008 Consider the following heuristic for planar Euclidean instances of the Traveling Salesman Problem (TSP): select a subset of the edges which induces a planar graph, and solve either the TSP or its graphical relaxation on that graph. In this paper, we give
Pearson, N, Letchford, A N
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On Optimal Beyond-Planar Graphs
Computing in Geometry and Topology, 2023 A graph is beyond-planar if it can be drawn in the plane with a specific restriction on crossings. Several types of beyond-planar graphs have been investigated, such as k-planar graphs where every edge is crossed at most k times and RAC graphs where ...
Franz Brandenburg
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Planar Graphs as VPG-Graphs [PDF]
Journal of Graph Algorithms and Applications, 2013 Summary: A graph is \(B_k\)-VPG when it has an intersection representation by paths in a rectangular grid with at most \(k\) bends (turns). It is known that all planar graphs are \(B_3\)-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are \(B_2\)-VPG.
Steven Chaplick, Torsten Ueckerdt
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Weak Degeneracy of Planar Graphs and Locally Planar Graphs
The Electronic Journal of Combinatorics, 2023 Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$-degenerate, then for any $(d+1)$-list assignment $L$ of $G$, one can construct an $L$ coloring of $G$ by a modified greedy coloring algorithm.
Ming Han +4 more
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