Results 11 to 20 of about 86,037 (264)
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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Polychromatic Colorings of Plane Graphs [PDF]
Discrete & Computational Geometry, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Noga Alon +7 more
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Bend-optimal orthogonal drawings of triconnected plane graphs
AKCE International Journal of Graphs and Combinatorics, 2018 A drawing of a plane graph G in which each edge is represented by a sequence of alternating horizontal and vertical line segments is called an orthogonal drawing.
Siddharth Bhatia, Kunal Lad, Rajiv Kumar
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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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Special Type Routing Problems in Plane Graphs
Mathematics, 2022 We considered routing problems for plane graphs to solve control problems of cutting machines in the industry. According to the cutting plan, we form its homeomorphic image in the form of a plane graph G.
Tatiana Makarovskikh, Anatoly Panyukov
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On embedding a cycle in a plane graph [PDF]
Discrete Mathematics, 2006 The problem of drawing a non-simple cycle as a non-intersecting closed curve into a planar graph drawn in the plane with the vertices represented as circles and the edges represented as thin stripes is considered. The problem is shown to have an interpretation in the \textit{clustered planarity}.
Pier Francesco Cortese +3 more
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Graphic Representation of a Dimensional Expansion of Triangular Fuzzy Number
Journal of Mathematics, 2021 We calculate Zadeh’s max-min composition operators for two 3-dimensional triangular fuzzy numbers. We prove that if the 3-dimensional result is limited to 2 dimensions, it is the same as the 2-dimensional result, which is shown as a graph.
Yong Sik Yun
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On the Upward Planarity of Mixed Plane Graphs
Journal of Graph Algorithms and Applications, 2014 A mixed plane graph is a plane graph whose edge set is partitioned into a set of directed edges and a set of undirected edges. An orientation of a mixed plane graph G is an assignment of directions to the undirected edges of G resulting in a directed ...
Fabrizio Frati +4 more
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A Survey on the Cyclic Coloring and its Relaxations
Discussiones Mathematicae Graph Theory, 2021 A cyclic coloring of a plane graph is a vertex coloring such that any two vertices incident with the same face receive distinct colors. This type of coloring was introduced more than fifty years ago, and a lot of research in chromatic graph theory was ...
Czap Július +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.
Ingo Althöfer +4 more
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