Results 11 to 20 of about 38,199 (317)
Planar median graphs and cubesquare-graphs [PDF]
Discrete Applied Mathematics, 2023 Median graphs are connected graphs in which for all three vertices there is a unique vertex that belongs to shortest paths between each pair of these three vertices. In this paper we provide several novel characterizations of planar median graphs.
Carsten R. Seemann +3 more
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On the planar edge-length ratio of planar graphs
Journal of Computational Geometry, 2020 The edge-length ratio of a straight-line drawing of a graph is the ratio between the lengths of the longest and of the shortest edge in the drawing. The planar edge-length ratio of a planar graph is the minimum edge-length ratio of any planar straight ...
Manuel Borrazzo, Fabrizio Frati
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Equitable Coloring of IC-Planar Graphs with Girth g ≥ 7
Axioms, 2023 An equitable k-coloring of a graph G is a proper vertex coloring such that the size of any two color classes differ at most 1. If there is an equitable k-coloring of G, then the graph G is said to be equitably k-colorable.
Danjun Huang, Xianxi Wu
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Connectivity of Planar Graphs [PDF]
Journal of Graph Algorithms and Applications, 2001 We give here three simple linear time algorithms on planar graphs: a 4-connexity test for maximal planar graphs, an algorithm enumerating the triangles and a 3-connexity test. Although all these problems got already linear-time solutions, the presented algorithms are both simple and efficient. They are based on some new theoretical results.
de Fraysseix, Hubert +1 more
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Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
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Drawing planar graphs with many collinear vertices
Journal of Computational Geometry, 2018 Consider the following problem: Given a planar graph $G$, what is the maximum number $p$ such that $G$ has a planar straight-line drawing with $p$ collinear vertices?
Giordano Da Lozzo +4 more
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A note on nearly Platonic graphs with connectivity one
Electronic Journal of Graph Theory and Applications, 2021 A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek,
Dalibor Froncek +3 more
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Theoretical Computer Science, 2018 We introduce the family of $k$-gap-planar graphs for $k \geq 0$, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most $k$ of its crossings. This definition is motivated by applications in edge casing, as a $k$-gap-planar graph can be drawn crossing-free after introducing ...
Sang Won Bae 0001 +10 more
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, 2013 In this paper, the concept of Total semirelib graph of a planar graph is introduced. Authors present a characterization of those graphs whose total semirelib graphs are planar, outer planar, Eulerian, hamiltonian with crossing number ...
Prasad, Manjunath +3 more
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SOME PROPERTIES ON COPRIME GRAPH OF GENERALIZED QUATERNION GROUPS
Barekeng, 2023 A coprime graph is a representation of finite groups on graphs by defining the vertex graph as an element in a group and two vertices adjacent to each other's if and only if the order of the two elements is coprime.
Arif Munandar
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