6 research outputs found
Intersection Graphs of Rays and Grounded Segments
We consider several classes of intersection graphs of line segments in the
plane and prove new equality and separation results between those classes. In
particular, we show that: (1) intersection graphs of grounded segments and
intersection graphs of downward rays form the same graph class, (2) not every
intersection graph of rays is an intersection graph of downward rays, and (3)
not every intersection graph of rays is an outer segment graph. The first
result answers an open problem posed by Cabello and Jej\v{c}i\v{c}. The third
result confirms a conjecture by Cabello. We thereby completely elucidate the
remaining open questions on the containment relations between these classes of
segment graphs. We further characterize the complexity of the recognition
problems for the classes of outer segment, grounded segment, and ray
intersection graphs. We prove that these recognition problems are complete for
the existential theory of the reals. This holds even if a 1-string realization
is given as additional input.Comment: 16 pages 12 Figure
ON THE MECHANISM OF THE RELAXATION PULSE GLOW DISCHARGE
Abstract. A mechanism of the low pressure relaxation glow discharge pulse is presented. Theoretical predictions and experimentally obtained values of discharges parameters are compared. The ion mobility, the secondary electron emission, the ionisation and the electrical parameters have a strong influence on the characteristics while the diffusion is of lesser importance