Results 31 to 40 of about 2,666,039 (345)
Colouring of plane graphs with unique maximal colours on faces [PDF]
, 2015 The Four Colour Theorem asserts that the vertices of every plane graph can be properly coloured with four colors. Fabrici and G\"oring conjectured the following stronger statement to also hold: the vertices of every plane graph can be properly coloured ...
Wendland, Alex
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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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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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Electronic Notes in Discrete Mathematics, 2009 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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Counting Plane Graphs: Cross-Graph Charging Schemes [PDF]
Combinatorics, probability & computing, 2012 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.
M. Sharir, Adam Sheffer
semanticscholar +1 more source
Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths [PDF]
, 2018 When can a plane graph with prescribed edge lengths and prescribed angles (from among $\{0,180^\circ, 360^\circ$\}) be folded flat to lie in an infinitesimally thin line, without crossings?
Abel, Zachary +5 more
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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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A Penrose polynomial for embedded graphs [PDF]
, 2011 We extend the Penrose polynomial, originally defined only for plane graphs, to graphs embedded in arbitrary surfaces. Considering this Penrose polynomial of embedded graphs leads to new identities and relations for the Penrose polynomial which can not be
Aigner +22 more
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A plane graph representation of triconnected graphs
Theoretical Computer Science, 2010 AbstractGiven a graph G=(V,E), a set S={s1,s2,…,sk} of k vertices of V, and k natural numbers n1,n2,…,nk such that ∑i=1kni=|V|, the k-partition problem is to find a partition V1,V2,…,Vk of the vertex set V such that |Vi|=ni, si∈Vi, and Vi induces a connected subgraph of G for each i=1,2,…,k. For the tripartition problem on a triconnected graph, a naive
Hiroshi Nagamochi +2 more
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