… chromatic number of a graph and, besides, many non-1-planar graphs are 6-… graph H such
that we already know that H is non-1-planar. As such a graph H, it is convenient to use graphs …

… -planar graph has a vertex of degree 6 and the connectivity cannot be larger than 6. (Recall
that the average degree of 1-planar graph is smaller than 8, and that the minimum degree is …

… 1-planar graphs do not always admit straight-line drawings [7]. They … minimal non-1planar
graphs [13]. The recognition problem of 1-planar graphs is NP-complete [12], even if the graph …

… non-1-planar graph G is minimal if the graph G − e is 1-planar for every edge e of G. We
construct two infinite families of minimal non-1-planar graphs … minimal non-1-planar graphs of …

… there are infinitely many minimal non-1-planar graphs and they … minimal non-1-planar graphs
of order n (compared to planar graphs, the number of n-vertex minimal nonplanar graphs is …

… A non-1-planar graph G is minimal if the graph urn:x-wiley:… infinite families of minimal
non-1-planar graphs and show that … -0003 nonisomorphic minimal non-1-planar graphs of order n. …

… 7 , which is tight for some graphs. They also provided tight lower bounds for the sizes …
graphs with minimum degree 4 or 5. In this paper, we show that any 1-planar graph with minimum …

… The class of k-planar graphs is not closed under edge contractions and already for k = 1
there are infinitely many minimal non-1-planar graphs, as shown by Korzhik [59]. …

… A minimal non- 1-planar graph is a graph that is not 1-planar … -isomorphic) minimal non-1-planar
graphs is exponential in n (… characterization of 1-planar graphs by Wagner-type theorem …

… Drawing planar graphs is an important topic in graph theory, combinatorics, and in particular
in graph drawing. The existence of straight-line drawings was independently proved by …