Results 21 to 30 of about 82,884 (244)
The plane-width of graphs [PDF]
Journal of Graph Theory, 2011 Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is the minimum diameter of the image of the vertex set over all such mappings.
Kaminski, Marcin +2 more
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Plane Graphs with Parity Constraints [PDF]
Graphs and Combinatorics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aichholzer Oswin +6 more
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Polychromatic Colorings of Plane Graphs [PDF]
Discrete & Computational Geometry, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alon, N. +7 more
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Journal of Graph Algorithms and Applications, 2008 Summary: In this paper we give a simple algorithm to generate all connected rooted plane graphs with at most m edges. A ``rooted'' plane graph is a plane graph with one designated (directed) edge on the outer face. The algorithm uses \(O(m)\) space and generates such graphs in \(O(1)\) time per graph on average without duplications.
Yamanaka, Katsuhisa, Nakano, Shin-Ichi
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Improved Bounds for Some Facially Constrained Colorings
Discussiones Mathematicae Graph Theory, 2023 A facial-parity edge-coloring of a 2-edge-connected plane graph is a facially-proper edge-coloring in which every face is incident with zero or an odd number of edges of each color. A facial-parity vertex-coloring of a 2-connected plane graph is a proper
Štorgel Kenny
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The total face irregularity strength of some plane graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A face irregular total -labeling of a 2-connected plane graph is a labeling of vertices and edges such that their face-weights are pairwise distinct. The weight of a face under a labeling is the sum of the labels of all vertices and edges surrounding ...
Meilin I. Tilukay +3 more
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Strong parity vertex coloring of plane graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A strong parity vertex coloring of a 2-connected plane graph is a coloring of the vertices such that every face is incident with zero or an odd number of vertices of each color.
Tomas Kaiser +3 more
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On the Hamiltonian Number of a Plane Graph
Discussiones Mathematicae Graph Theory, 2019 The Hamiltonian number of a connected graph is the minimum of the lengths of the closed spanning walks in the graph. In 1968, Grinberg published a necessary condition for the existence of a Hamiltonian cycle in a plane graph, formulated in terms of the ...
Lewis Thomas M.
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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. This paper focuses on rook-drawings of planar graphs. We first give a linear algorithm to compute a planar
Auber, David +3 more
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Rook-Drawing for Plane Graphs [PDF]
, 2015 Motivated by visualization of large graphs, 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. This paper focuses on rook-drawings of planar graphs. We first give a
Auber, David +3 more
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