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Facial Rainbow Coloring of Plane Graphs
Discussiones Mathematicae Graph Theory, 2019 A vertex coloring of a plane graph G is a facial rainbow coloring if any two vertices of G connected by a facial path have distinct colors. The facial rainbow number of a plane graph G, denoted by rb(G), is the minimum number of colors that are necessary
Jendroľ Stanislav, Kekeňáková Lucia
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Unique-Maximum Coloring Of Plane Graphs
Discussiones Mathematicae Graph Theory, 2016 A unique-maximum k-coloring with respect to faces of a plane graph G is a coloring with colors 1, . . . , k so that, for each face of G, the maximum color occurs exactly once on the vertices of α.
Fabrici Igor, Göring Frank
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Splitting Plane Graphs to Outerplanarity
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 ...
Gronemann, Martin +2 more
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Zig-zag facial total-coloring of plane graphs [PDF]
Opuscula Mathematica, 2018 In this paper we introduce the concept of zig-zag facial total-coloring of plane graphs. We obtain lower and upper bounds for the minimum number of colors which is necessary for such a coloring.
Július Czap +2 more
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Folding Equilateral Plane Graphs [PDF]
International Journal of Computational Geometry & Applications, 2011 We consider two types of folding applied to equilateral plane graph linkages. First, under continuous folding motions, we show how to reconfigure any linear equilateral tree (lying on a line) into a canonical configuration. By contrast, it is known that such reconfiguration is not always possible for linear (nonequilateral) trees and for (nonlinear ...
Abel, Zachary Ryan +6 more
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Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)
Journal of Mathematics, 2021 In this study, we used grids and wheel graphs G=V,E,F, which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set.
Aleem Mughal, Noshad Jamil
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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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Ars Mathematica Contemporanea, 2015 Summary: A plane graph is called alternating if all adjacent vertices have different degrees, and all neighboring faces as well. Alternating plane graphs were introduced in 2008. This paper presents the previous research on alternating plane graphs.{ }There are two smallest alternating plane graphs, having 17 vertices and 17 faces each.
Althöfer, Ingo +4 more
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Colorings of Plane Graphs Without Long Monochromatic Facial Paths
Discussiones Mathematicae Graph Theory, 2021 Let G be a plane graph. A facial path of G is a subpath of the boundary walk of a face of G. We prove that each plane graph admits a 3-coloring (a 2-coloring) such that every monochromatic facial path has at most 3 vertices (at most 4 vertices).
Czap Július +2 more
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Domination number of annulus triangulations
Theory and Applications of Graphs, 2020 An {\em annulus triangulation} $G$ is a 2-connected plane graph with two disjoint faces $f_1$ and $f_2$ such that every face other than $f_1$ and $f_2$ are triangular, and that every vertex of $G$ is contained in the boundary cycle of $f_1$ or $f_2$.
Toshiki Abe +2 more
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