Results 11 to 20 of about 543,681 (314)
Reflexive edge strength of convex polytopes and corona product of cycle with path
AIMS Mathematics, 2022 For a graph $ G $, we define a total $ k $-labeling $ \varphi $ is a combination of an edge labeling $ \varphi_e(x)\to\{1, 2, \ldots, k_e\} $ and a vertex labeling $ \varphi_v(x) \to \{0, 2, \ldots, 2k_v\} $, such that $ \varphi(x) = \varphi_v(x) $ if ...
Kooi-Kuan Yoong +4 more
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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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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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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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Facial rainbow edge-coloring of simple 3-connected plane graphs [PDF]
Opuscula Mathematica, 2020 A facial rainbow edge-coloring of a plane graph \(G\) is an edge-coloring such that any two edges receive distinct colors if they lie on a common facial path of \(G\).
Július Czap
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Plane Graphs with Parity Constraints [PDF]
Graphs and Combinatorics, 2009 Let S be a set of n points in general position in the plane. Together with S we are given a set of parity constraints, that is, every point of S is labeled either even or odd. A graph G on S satisfies the parity constraint of a point p¿¿¿S, if the parity of the degree of p in G matches its label.
Aichholzer Oswin +6 more
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Graph polynomials and paintability of plane graphs
Discrete Applied Mathematics, 2022 There exists a variety of coloring problems for plane graphs, involving vertices, edges, and faces in all possible combinations. For instance, in the \emph{entire coloring} of a plane graph we are to color these three sets so that any pair of adjacent or incident elements get different colors.
Jarosław Grytczuk +2 more
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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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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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BgNet: Classification of benign and malignant tumors with MRI multi-plane attention learning
Frontiers in Oncology, 2022 ObjectivesTo propose a deep learning-based classification framework, which can carry out patient-level benign and malignant tumors classification according to the patient’s multi-plane images and clinical information.MethodsA total of 430 cases of spinal
Hong Liu +17 more
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