Open AccessJournal Article
The coarseness of a graph
Lowell W. Beineke,Gary Chartrand +1 more
TLDR
In this article, the conditions générales d'utilisation (http://www.compositio.org/conditions) of the agreement with the Foundation Compositio Mathematica are described.Abstract:
© Foundation Compositio Mathematica, 1968, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.read more
Citations
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Journal ArticleDOI
Graphs with Forbidden Subgraphs
TL;DR: In this paper, a unified way, several classes of graphs which can be defined in terms of the kinds of subgraphs they do not contain, and related concepts are investigated.
Journal ArticleDOI
On Drawings and Decompositions of 1-Planar Graphs
Július Czap,Dávid Hudák +1 more
TL;DR: It is demonstrated that each subgraph of an optimal 1-planar graph can be decomposed into a planar graph and a forest, and an upper bound on the number of edges of bipartite 1- Planar graphs is derived.
Journal ArticleDOI
Non-planar core reduction of graphs
Markus Chimani,Carsten Gutwenger +1 more
TL;DR: A reduction method is presented that reduces a graph to a smaller core graph which behaves invariant with respect to non-planarity measures like crossing number, skewness, coarseness, and thickness and has applications in heuristic and exact optimization algorithms for the non-Planarity measures.
Computing crossing numbers
TL;DR: This thesis shows how to formulate the crossing number problem as systems of linear inequalities, and discusses how to solve these formulations for reasonably sized graphs to provable optimality in acceptable time—despite its theoretical complexity class.
On drawings and decompositions of 1-planar graphs
TL;DR: In this paper, it was shown that every 1-planar drawing of any 1-plansar graph on n vertices has at most n 2 crossings, and this bound is tight.