The notion of 1-planarity is among the most natural and most studied generalizations of
graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at …

After a brief historical account, a few simple structural theorems about plane graphs useful
for coloring are stated, and two simple applications of discharging are given. Afterwards, the …

A graph is called 1-planar if it can be drawn in the plane so that each its edge is crossed by
at most one other edge. In the paper, we study the existence of subgraphs of bounded …

A graph is 1‐planar if it can be drawn on the plane so that each edge is crossed by no more
than one other edge (and any pair of crossing edges cross only once). A non‐1‐planar …

A queue layout of a graph consists of a total order of the vertices, and a partition of the edges
into queues, such that no two edges in the same queue are nested. The minimum number of …

A plane graph is a graph embedded in a plane without edge crossings. Fáry's theorem
states that every plane graph can be drawn as a straight-line drawing, preserving the …

A Right Angle Crossing Graph (also called a RAC graph for short) is a graph that has a
straight-line drawing where any two crossing edges are orthogonal to each other. A 1-planar …

It is known that the acyclic chromatic number of a subcubic graph is at most four, and its
acyclic edge chromatic number is at most five. We present algorithms that prove these two …

On edge colorings of 1-planar graphs Page 1 Information Processing Letters 111 (2011) 124–128
Contents lists available at ScienceDirect Information Processing Letters www.elsevier.com/locate/ipl …

A\emph (k, t)-track layout of a graph G consists of a (proper) vertex t-colouring of G, a total
order of each vertex colour class, and a (non-proper) edge k-colouring such that between …