Journal of Graph Algorithms and Applications
https://jgaa.info/index.php/jgaa
<p>The <span class="emph">Journal of Graph Algorithms and Applications</span> (<span class="emph">JGAA</span>) is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. <span class="emph">JGAA</span> is supported by distinguished advisory and editorial boards, has high scientific standards and is distributed in electronic form. <span class="emph">JGAA</span> is a diamond open access journal that charges no author fees.</p>Brown Universityen-USJournal of Graph Algorithms and Applications1526-1719Min-$k$-planar Drawings of Graphs
https://jgaa.info/index.php/jgaa/article/view/2925
<p>The study of nonplanar drawings of graphs with restricted crossing configurations is a well-established topic in graph drawing, often referred to as <em>beyond-planar graph drawing</em>. One of the most studied types of drawings in this area are the <em>$k$-planar drawings</em> $(k \geq 1)$, where each edge cannot cross more than $k$ times. We generalize $k$-planar drawings, by introducing the new family of <em>min-$k$-planar drawings.</em> In a min-$k$-planar drawing edges can cross an arbitrary number of times, but for any two crossing edges, one of the two must have no more than $k$ crossings. We prove a general upper bound on the number of edges of min-$k$-planar drawings, a finer upper bound for $k=3$, and tight upper bounds for $k=1,2$. Also, we study the inclusion relations between min-$k$-planar graphs (i.e., graphs admitting min-$k$-planar drawings) and $k$-planar graphs.<br />In our setting, we only allow <em>simple</em> drawings, that is, any two edges cross at most once, no two adjacent edges cross, and no three edges intersect at a common point.</p>Carla BinucciAaron BüngenerGiuseppe Di BattistaWalter DidimoVida DujmovićSeok-Hee HongMichael KaufmannGiuseppe LiottaPat MorinAlessandra Tappini
Copyright (c) 2024 Carla Binucci, Aaron B\"ungener, Giuseppe Di Battista, Walter Didimo, Vida Dujmovi\'c, Seok-Hee Hong, Michael Kaufmann, Giuseppe Liotta, Pat Morin, Alessandra Tappini
https://creativecommons.org/licenses/by/4.0
2024-05-172024-05-1728213510.7155/jgaa.v28i2.2925