Results 51 to 60 of about 200,785 (277)
The strong chromatic index of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe chromatic index $\chi'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors.
Yiqiao Wang +3 more
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Neighbor Product Distinguishing Total Colorings of Planar Graphs with Maximum Degree at least Ten
Discussiones Mathematicae Graph Theory, 2021 A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2, . . . , k}. Let p(u) denote the product of the color on a vertex u and colors on all the edges incident with u.
Dong Aijun, Li Tong
doaj +1 more source
Bar 1-Visibility Drawings of 1-Planar Graphs
, 2013 A bar 1-visibility drawing of a graph $G$ is a drawing of $G$ where each vertex is drawn as a horizontal line segment called a bar, each edge is drawn as a vertical line segment where the vertical line segment representing an edge must connect the ...
A.M. Dean +13 more
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Unique Triangulated 1-Planar Graphs
, 2023 It is well-known that every 3-connected planar graph has a unique planar embedding on the sphere. We study the extension to triangulated 1-planar graphs, T1P graphs for short, which admit an embedding in which each edge is crossed at most once and each face is a triangle, and obtain an algorithmic solution by a cubic time recognition algorithm that ...
openaire +2 more sources
The maximum number of edges of bipartite 1-planar graphs with 1-disk drawings
AKCE International Journal of Graphs and CombinatoricsA graph is 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Let G be a bipartite 1-planar graph with bipartition sets X and Y. A 1-disk [Formula: see text] drawing of G is a 1-planar drawing such that all vertices
Guiping Wang
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Discrete Mathematics & Theoretical Computer ScienceNot every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward $k$-planar drawings of DAGs in which the
Patrizio Angelini +10 more
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Structure of Projective Planar Subgraphs of the Graph Obstructions for Fixed Surface
Кібернетика та комп'ютерні технології, 2022 Consider the problem of studying the metric properties of a subgraph G \ v, where v is an arbitrary vertex of obstruction graphs G of a nonorientable genus, which will determine the sets of points of attachment of one subgraph to another and allow ...
Volodymyr Petrenjuk +2 more
doaj +1 more source
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective To delineate specific in vivo white matter pathology in neuronal intranuclear inclusion disease (NIID) using diffusion spectrum imaging (DSI) and define its clinical relevance. Methods DSI was performed on 42 NIID patients and 38 matched controls.
Kaiyan Jiang +10 more
wiley +1 more source
Negative results on acyclic improper colorings [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Raspaud and Sopena showed that the oriented chromatic number of a graph with acyclic chromatic number $k$ is at most $k2^{k-1}$. We prove that this bound is tight for $k \geq 3$.
Pascal Ochem
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Recognizing and Drawing IC-planar Graphs
, 2015 IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs.
C Auer +27 more
core +1 more source