Results 1 to 10 of about 30,355,443 (292)

Stack and Queue Layouts via Layered Separators

Journal of Graph Algorithms and Applications, 2018
It is known that every proper minor-closed class of graphs has bounded stack-number (a.k.a. book thickness and page number). While this includes notable graph families such as planar graphs and graphs of bounded genus, many other graph families are not
Vida Dujmović, Fabrizio Frati
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
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A note on the coprime graph of a group [PDF]

International Journal of Group Theory, 2016
In this paper we study the coprime graph of a group $G$. The coprime graph of a group $G$, is a graph whose vertices are elements of $G$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$.
Hamid Reza Dorbidi
doaj  

Large matchings in maximal 1-planar graphs

Discrete Mathematics
It is well-known that every maximal planar graph has a matching of size at least $\tfrac{n+8}{3}$ if $n\geq 14$. In this paper, we investigate similar matching-bounds for maximal \emph{1-planar} graphs, i.e., graphs that can be drawn such that every edge has at most one crossing.
Therese Biedl, John Wittnebel
openaire   +3 more sources

On 1-Planar Graphs with Bounded Cop-Number

Theoretical Computer Science
Cops and Robbers is a type of pursuit-evasion game played on a graph where a set of cops try to capture a single robber. The cops first choose their initial vertex positions, and later the robber chooses a vertex. The cops and robbers make their moves in alternate turns: in the cops' turn, every cop can either choose to move to an adjacent vertex or ...
Prosenjit Bose, Jean-Lou De Carufel, Anil Maheshwari, Karthik Murali 0001   +3 more
openaire   +5 more sources

Regularity and Planarity of Token Graphs

Discussiones Mathematicae Graph Theory, 2017
Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G.
Carballosa Walter, Fabila-Monroy Ruy, Leaños Jesús, Rivera Luis Manuel   +3 more
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On the d-independence number in 1-planar graphs

Graphs and Combinatorics
The $d$-independence number of a graph $G$ is the largest possible size of an independent set $I$ in $G$ where each vertex of $I$ has degree at least $d$ in $G$. Upper bounds for the $d$-independence number in planar graphs are well-known for $d=3,4,5$, and can in fact be matched with constructions that actually have minimum degree $d$.
Therese Biedl, Prosenjit Bose, Babak Miraftab   +2 more
openaire   +3 more sources

Min-$k$-planar Drawings of Graphs

Journal of Graph Algorithms and Applications
The study of nonplanar drawings of graphs with restricted crossing configurations is a well-established topic in graph drawing, often referred to as beyond-planar graph drawing.
Carla Binucci, Aaron Büngener, Giuseppe Di Battista, Walter Didimo, Vida Dujmović, Seok-Hee Hong, Michael Kaufmann, Giuseppe Liotta, Pat Morin, Alessandra Tappini   +9 more
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Strong oriented chromatic number of planar graphs without short cycles

Discrete Mathematics & Theoretical Computer Science, 2008
Let M be an additive abelian group. A strong oriented coloringof an oriented graph G is a mapping φ from V(G) to M such that (1) φ(u) ≠ φ(v) whenever uv is an arc in G and (2) φ(v) - φ(u) ≠ -(φ(t) - φ(z)) whenever uv and zt are two arcs in
Mickaël Montassier, Pascal Ochem, Alexandre Pinlou   +2 more
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On the discrete Fréchet distance in a graph

Journal of Computational Geometry
The Fréchet distance is a well-studied similarity measure between curves that is widely used throughout computer science. Motivated by applications where curves stem from paths and walks on an underlying graph (such as a road network), we define and ...
Anne Driemel, Ivor van der Hoog, Eva Rotenberg   +2 more
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