Results 71 to 80 of about 30,213,529 (145)

Improvements on the density of maximal 1‐planar graphs [PDF]

Journal of Graph Theory, 2017
AbstractA graph is 1‐planar if it can be drawn in the plane such that each edge is crossed at most once. A graph, together with a 1‐planar drawing is called 1‐plane. A graph is maximal 1‐planar (1‐plane), if we cannot add any missing edge so that the resulting graph is still 1‐planar (1‐plane). Brandenburg et al.
János Barát, Géza Tóth 0001
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Structural Parameterizations of $k$-Planarity

Journal of Graph Algorithms and Applications
The concept of $k$-planarity is extensively studied in the context of Beyond Planarity. A graph is $k$-planar if it admits a drawing in the plane in which each edge is crossed at most $k$ times.
Tatsuya Gima, Yasuaki Kobayashi, Yuto Okada   +2 more
doaj   +1 more source

$1$-string $B_2$-VPG representation of planar graphs

Journal of Computational Geometry, 2016
In this paper, we prove that every planar graph has a 1-string $B_2$-VPG representation—a string representation using paths in a rectangular grid that contain at most two bends.
Therese Biedl, Martin Derka
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The Basis Number of 1-Planar Graphs

Annals of Combinatorics
Let $B$ be a set of Eulerian subgraphs of a graph $G$. We say $B$ forms a $k$-basis if it is a minimum set that generates the cycle space of $G$, and any edge of $G$ lies in at most $k$ members of $B$. The basis number of a graph $G$, denoted by $b(G)$, is the smallest integer such that $G$ has a $k$-basis. A graph is called 1-planar (resp.
Saman Bazargani, Therese Biedl, Prosenjit Bose, Anil Maheshwari, Babak Miraftab   +4 more
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The strong chromatic index of 1-planar graphs [PDF]

Discrete Mathematics & Theoretical Computer Science
The 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, Ning Song, Jianfeng Wang, Weifan Wang   +3 more
doaj   +1 more source

Joins of 1-planar graphs [PDF]

Acta Mathematica Sinica, English Series, 2014
A graph is called 1-planar if there exists its drawing in the plane such that each edge is crossed at most once. In this paper, we study 1-planar graph joins. We prove that the join $G+H$ is 1-planar if and only if the pair $[G,H]$ is subgraph-majorized (that is, both $G$ and $H$ are subgraphs of graphs of the major pair) by one of pairs $[C_3 \cup C_3,
Czap, Július, Hudák, Dávid, Madaras, Tomáš   +2 more
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Negation Switching Equivalence in Signed Graphs [PDF]

, 2010
Unless mentioned or defined otherwise, for all terminology and notion in graph theory the reader is refer to [8].
Reddy, Siva Kota
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Upward Embeddings and Orientations of Undirected Planar Graphs

Journal of Graph Algorithms and Applications, 2003
An upward embedding of an embedded planar graph specifies, for each vertex v, which edges are incident on v "above" or "below" and, in turn, induces an upward orientation of the edges from bottom to top.
Walter Didimo, Maurizio Pizzonia
doaj   +1 more source

Heuristics for Exact 1-Planarity Testing

Journal of Graph Algorithms and Applications
Since many real-world graphs are nonplanar, the study of graphs that allow few crossings per edge has been an active subfield of graph theory in recent years.
Miriam Münch, Simon D. Fink, Matthias Pfretzschner, Ignaz Rutter   +3 more
doaj   +1 more source

Minimizing the oriented diameter of a planar graph [PDF]

, 2009
We consider the problem of minimizing the diameter of an orientation of a planar graph. A result of Chvátal and Thomassen shows that for general graphs, it is NP-complete to decide whether a graph can be oriented so that its diameter is at most two.
Noble, SD, Noble, Steven, Eggemann, N, Eggemann, N.   +3 more
core   +1 more source