Results 1 to 10 of about 1,410,460 (300)
On the Upward Planarity of Mixed Plane Graphs [PDF]
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
doaj +2 more sources
Zig-zag facial total-coloring of plane graphs [PDF]
Opuscula Mathematica, 2018 In this paper we introduce the concept of zig-zag facial total-coloring of plane graphs. We obtain lower and upper bounds for the minimum number of colors which is necessary for such a coloring.
Július Czap +2 more
doaj +1 more source
Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)
Journal of Mathematics, 2021 In this study, we used grids and wheel graphs G=V,E,F, which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set.
Aleem Mughal, Noshad Jamil
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +2 more sources
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
doaj +1 more source
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
doaj +1 more source
Minimal unavoidable sets of cycles in plane graphs [PDF]
Opuscula Mathematica, 2018 A set \(S\) of cycles is minimal unavoidable in a graph family \(\cal{G}\) if each graph \(G \in \cal{G}\) contains a cycle from \(S\) and, for each proper subset \(S^{\prime}\subset S\), there exists an infinite subfamily \(\cal{G}^{\prime}\subseteq\cal{
Tomáš Madaras, Martina Tamášová
doaj +1 more source