Results 31 to 40 of about 391,866 (285)
On d-antimagic labelings of plane graphs
Electronic Journal of Graph Theory and Applications, 2013 The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face.
Martin Baca +4 more
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On facial unique-maximum (edge-)coloring [PDF]
, 2017 A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face $\alpha$ the maximal color appears exactly once on the vertices of $\alpha$.
Andova, Vesna +4 more
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Facial graceful coloring of plane graphs [PDF]
Opuscula MathematicaLet \(G\) be a plane graph. Two edges of \(G\) are facially adjacent if they are consecutive on the boundary walk of a face of \(G\). A facial edge coloring of \(G\) is an edge coloring such that any two facially adjacent edges receive different colors ...
Július Czap
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Facial [r,s,t]-Colorings of Plane Graphs
Discussiones Mathematicae Graph Theory, 2019 Let G be a plane graph. Two edges are facially adjacent in G if they are consecutive edges on the boundary walk of a face of G. Given nonnegative integers r, s, and t, a facial [r, s, t]-coloring of a plane graph G = (V,E) is a mapping f : V ∪ E → {1, . .
Czap Július +3 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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A simple and elementary proof of Whitney's unique embedding theorem
, 2020 In this note we give a short and elementary proof of a more general version of Whitney's theorem that 3-connected planar graphs have a unique embedding in the plane.
Brinkmann, Gunnar
core +1 more source
On the dimension of Archimedean solids [PDF]
Opuscula Mathematica, 2014 We study the dimension of graphs of the Archimedean solids. For most of these graphs we find the exact value of their dimension by finding unit-distance embeddings in the euclidean plane or by proving that such an embedding is not possible.
Tomáš Madaras, Pavol Široczki
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Triangle-free intersection graphs of line segments with large chromatic number [PDF]
, 2012 In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no.
Arkadiusz Pawlik +20 more
core +1 more source
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
openaire +2 more sources
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
openaire +2 more sources