Results 1 to 10 of about 568,500 (305)
Even cycles and perfect matchings in claw-free plane graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Lov{\'a}sz showed that a matching covered graph $G$ has an ear decomposition starting with an arbitrary edge of $G$. Let $G$ be a graph which has a perfect matching.
Shanshan Zhang +2 more
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Edge partitions of optimal 2-plane and 3-plane graphs [PDF]
, 2019 A topological graph is a graph drawn in the plane. A topological graph is $k$-plane, $k>0$, if each edge is crossed at most $k$ times. We study the problem of partitioning the edges of a $k$-plane graph such that each partite set forms a graph with a ...
Michael A. Bekos +5 more
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Splitting Plane Graphs to Outerplanarity [PDF]
Journal of Graph Algorithms and Applications, 2023 Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often planarity, for which the problem is NP-hard.Here we study how to minimize the number of splits to turn a plane graph ...
Martin Gronemann +2 more
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The total face irregularity strength of some plane graphs [PDF]
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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Counting Plane Graphs: Cross-Graph Charging Schemes [PDF]
Combinatorics, Probability and Computing, 2013 We study cross-graph charging schemes for graphs drawn in the plane. These are charging schemes where charge is moved across vertices of different graphs. Such methods have recently been used to obtain various properties of triangulations that are embedded in a fixed set of points in the plane.
Micha Sharir, Adam Sheffer
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New Results of Face Labeling for Some Plane Graphs
IEEE Access, 2019 A labeling of a plane graph is called super d-antimagic if the vertices receive the smallest labels and the weight set of all faces in an arithematic progression with difference d, where weight of each face is the some of all labels correspond to that ...
Nabila Hameed +4 more
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Journal of Graph Algorithms and Applications, 2009 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.
Katsuhisa Yamanaka, Shin-ichi Nakano
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Polychromatic Colorings of Plane Graphs [PDF]
Discrete & Computational Geometry, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Noga Alon +7 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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3-Facial Coloring of Plane Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2008 A plane graph is l-facially k-colourable if its vertices can be coloured with k colours such that any two distinct vertices on a facial segment of length at most l are coloured differently. We prove that every plane graph is 3-facially 11-colourable.
Frédéric Havet +2 more
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