arXiv subjects

Maria Eleni Pavlidi

Publications and source records attributed to Maria Eleni Pavlidi.

6 recordsLinked to original sources

arXiv2026

On the $2$-Bend Slope Number of $1$-Planar Graphs

While drawing planar graphs with few slopes and few bends is a well-studied problem, corresponding extensions to beyond-planar graphs still remain mostly unexplored. Motivated by this observation, in this work, we provide bounds on the slope number of biconnected $1$-planar graphs when two bends are allowed along each edge. Our contribution is an incremental drawing algorithm that produces $2$-bend $1$-planar drawings of biconnected $1$-plane graphs with maximum degree $Δ$ using any prescribed set of $Δ$ pairwise distinct slopes.

cs.CG↗

arXiv2026

On the Recognition of Outerplanar Graphs with Queue Number 1

A linear layout of a graph is defined as a total order of the vertices and a partition of the edges to pages. In a stack (queue) layout, no two edges on the same page may cross (nest). The stack (queue) number of a graph is the minimum number of pages required in a stack (queue) layout. This paper focuses on characterizing and recognizing graphs that have both stack number 1 and queue number 1. It is known that the graphs with stack number 1 are exactly the outerplanar graphs. We show that (i) deciding whether a given outerplanar graph has queue number 1 is NP-hard; (ii) deciding whether a given maximal outerplanar graph has queue number 1 can be done in linear time. Moreover, we investigate the interplay between outerpaths with queue number 1 and their maximum vertex degree.

cs.CG↗

arXiv2026

Weighted Book Thickness

We introduce and study the weighted book thickness of graphs. A $k$-page book embedding of a graph $G=(V,E)$ is defined by a spanning cycle $C$ for $V$ (which does not need to be part of $G$) and a partition $E=\bigcup_{i=1}^{k}E_i$ such that $E\cap C\subseteq E_1$ and each graph $G_i=(V,E_i\cup C)$, for $1 \le i \le k$, is outerplane with outer cycle $C$. If $e\in E_i$, we say that $e$ appears on Page $i$. The classical book thickness of a graph $G$ is the minimum $k$ such that there exists a $k$-page book embedding of $G$, that is, the minimum (over all book embeddings of $G$) achievable maximum page an edge appears on. In contrast, the weighted book thickness is the minimum achievable average page an edge appears on. The embeddings that realize weighted book thickness can differ from those that realize (classical) book thickness. We show that, although every planar graph on at most nine vertices admits a 2-page book embedding realizing its weighted book thickness, already for ten vertices, there is a planar graph for which every realization of its weighted book thickness needs more pages than its book thickness. We prove that there even exists a 2-tree whose weighted book thickness cannot be realized on two pages. On the positive side, we show that for every graph of pathwidth at most two, the weighted book thickness can always be realized by a 2-page book embedding and such an embedding can be found in linear time. Moreover, we prove that it is NP-complete to decide if the weighted book thickness is at most $k$, for some given integer $k$.

cs.CG↗

arXiv2026

Stack and Queue Layouts with Defects

Linear layouts of graphs -- particularly \emph{stack} and \emph{queue} layouts -- are well-established types of representations in graph drawing, thanks to their connection with numerous theoretical and practical problems. In such layouts, all vertices are linearly ordered and the edges are partitioned into sets that avoid specific forbidden configurations: in a stack layout no two independent edges within the same set cross, whereas in a queue layout no two independent edges within the same set are nested. A central problem in this context is to determine, for a given graph $G$, its \emph{stack number} or \emph{queue number}, that is, the minimum number of sets into which the edges can be partitioned so that a corresponding stack or queue layout of $G$ exists. In this work, we introduce a relaxation of stack and queue layouts, which allows some forbidden patterns for the edges in the same set. Namely, for a given integer $k > 0$, a \emph{$k$-defective stack layout} (resp. a \emph{$k$-defective queue layout}) allows an edge to be in a crossing (resp. nesting) relationship with at most~$k$ edges within the same set. Our motivation is to extend the classes of graphs that admit linear layouts using a limited number of edge-partition sets, at the cost of allowing some defects. We study defective linear layouts both from a combinatorial and from an algorithmic perspective, providing an array of results across different graph classes and parameters.

cs.CG↗

arXiv2026

How Many Slopes Does Polynomial Area Cost?

In this work, we study the interplay between the number of slopes, the number of bends per edge, and the area requirements for planar drawings of bounded-degree graphs. Our motivation stems from the fact that, while numerous algorithms produce planar drawings with few slopes for graphs of relatively small degree in polynomial area, existing approaches for higher-degree graphs often require super-polynomial area. We address this gap in the literature by presenting new constructions that yield polynomial-area drawings with few bends per edge while slightly increasing the required number of slopes, thereby providing the first systematic study of slopes, bends and area trade-offs.

cs.CG↗

arXiv2023

On the Deque and Rique Numbers of Complete and Complete Bipartite Graphs

Several types of linear layouts of graphs are obtained by leveraging known data structures; the most notable representatives are the stack and the queue layouts. In this content, given a data structure, one seeks to specify an order of the vertices of the graph and a partition of its edges into pages, such that the endpoints of the edges assigned to each page can be processed by the given data structure in the underlying order. In this paper, we study deque and rique layouts of graphs obtained by leveraging the double-ended queue and the restricted-input double-ended queue (or deque and rique, for short), respectively. Hence, they generalize both the stack and the queue layouts. We focus on complete and complete bipartite graphs and present bounds on their deque- and rique-numbers, that is, on the minimum number of pages needed by any of these two types of linear layouts.

cs.DS↗